Maths-
General
Easy
Question
The quadratic equation whose roots are I and m where l=
is
Hint:
In this question, we have to find the quadratic equation where the roots l and m are given. First we will find the value of l and m. Then to find the quadratic equation when l and m are roots we will use the form
.
The correct answer is: ![x squared minus 5 x plus 6 equals 0](data:image/png;base64,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)
Given, the quadratic equation whose roots are I and m where
l =![lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses](data:image/png;base64,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)
![l equals limit as theta rightwards arrow 0 of open parentheses fraction numerator 3 space sin theta minus 4 sin cubed theta over denominator theta end fraction close parentheses space space space space space space space space space space space space space space space space space space space space m equals limit as theta rightwards arrow 0 of open parentheses fraction numerator 2 tan theta over denominator theta left parenthesis 1 minus tan squared theta right parenthesis end fraction close parentheses
space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin space 3 theta over denominator theta end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator tan space 2 theta over denominator theta end fraction close parentheses
space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin space 3 theta over denominator 3 theta end fraction close parentheses cross times 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of space open parentheses fraction numerator sin 2 theta over denominator theta cos 2 theta end fraction close parentheses
space equals 1 cross times 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as theta rightwards arrow 0 of open parentheses fraction numerator sin 2 theta over denominator 2 theta end fraction close parentheses cross times 2 cross times fraction numerator 1 over denominator cos 2 theta end fraction
space equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2
l equals 3 space a n d space m equals 2
t h e space q u a d t r a t i c space e q u a t i o n space w h e n space t h e space r o o t s space a r e space g i v e n
equals x squared minus left parenthesis l plus m right parenthesis x plus l m
equals x squared minus left parenthesis 3 plus 2 right parenthesis x plus left parenthesis 3 cross times 2 right parenthesis
equals x squared minus 5 x plus 6 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)
Related Questions to study
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Is equal to
Is equal to
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is equal to
is equal to
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Maths-
If ![f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root comma text then end text L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,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)
If ![f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root comma text then end text L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,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)
Maths-General
maths-
maths-General
Maths-
If
then the values of a and b are
If
then the values of a and b are
Maths-General
Maths-
Maths-General
Maths-
If
then k=
If
then k=
Maths-General
maths-
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANUAAAArCAYAAADv2M3qAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABZVJREFUeNrtnXFkX1cUx6+Yn5kIFTUVU2qqpiLUVMXsn6qKqAj7I3/MVKiZmpoRNTUzI/ZHTU2pqIqqEhUzVaMmIiJGRVXNlJiZmAj7Y6Yqwm/3yPc3Lzf3vnvf77173u+9dz4cyXv3l989v/POvffc817OTylBOEgbsqNlVcvbYhJBKIY+LZ9oWRdTCE2AnH2Wqa9XYu7/mYXthZoxrGWNqa/3tSyLyfeximvAwkuEDGVzXMs1LU9rfFFHGPo5gr6ONcBnsnBKywpHR7SZfeZpX2X60He1XMJmu26MMNmRJqaHGFhl+Uwvs4LBFZUJLfdT2ie13GP+4HUcVN9qucywQj3SMhDZ5j6f6WVf+JRjT/ullpmUtnZCZmoyqEax36CN/B9aPjTax7X8qvZS0/TzguU9KLRaQhjUDtD5Jy3vWc5TCPWVli30R6HvUeM10w5H+BptHWhAnWCwOfnFF9D7L9hxybI6hupdpC/0YwLbhD0XtRxKtJ/R8nNsB17AzNNte9UGFYVh2/hMfQiXkivxaS0bWk7i+CSOzxjv88Qx2Fz8o6VlOU+h2g1c+L4Ue1N6/M3E8UUt31vsZkoMmy/AJjMJva87Vq8QvYvSqx/9fYPVmuz9OSbJDi1ci6i80DKU0v6bZeas8qB6gBAgrX3csnL9YNmoH8rQ767l3BQcNMm8ljHLa8/DcYmzEWbbdkafecc4N+Bw1rx6Z9FrFhOUj52YzkszzL+e9pcl7D/aga/xiWvFGMi4othmtwkkHqZyDKolywq4nDKJPVZ7qXIKEQcLsHE39nP5xOspK0AWvfPotR040UUdVKdxYdPal3t0UMV673aGC0Hhxhz2Xce7CP/MtLRvkrsCPYZLtLnLZ9L2Knn0DtXrXRWWLo8e/tEse8fTPl+zQbVd0EqV5KryPxL0GAkSUxczgbKeklx5gFBqqkSbu3zmM7V3j7FovUP1GkNSwkf0RMUNbBxdfKfip4G5B9VcwJ7qgiXUW/SEyb6QwpZS30TY1OEa+jehTOOPWt7A6vikgPCvW5vbfIYmHbpvdSSC3qF6ncL+38dlXItoLGIj6YKyNLdrNqjoQlMafRKDYcj4jBRGbCQ24sM4Hk15z2lPGE3Ybv5SavkW9KB9FGUhHxmvOYxzg0bi5G5JNl9EouIsjodw7mIkvbP4Au3ZKPP3GqKRK5brFv3m798pm8EWHGszccwxmLpNCWeBHPwXJA+eWlamccx6tPo8V/YUd0e/XThPyBMMa5Z9Bd3vWcAqRavWVqK/FhzWlp2975kQY7EFe71I2G/CsnKVofdbyAHsYuWctqxmK0qoFSEP1B4WM0WD9YFagY+PFd+/fgj797SXxAyCIAiCIAiChXZFpKp6i9RfBEEQBEEQBEEQBEHocaTardBzcBbNzIOvyKRUuxV6As6imUUQ8kycVLstYOkX8jnpSIX09T293fhqt9xloUJKbDUJrqKZReP6PyOOareVgLMsVGiJrabAUTQzBrYikxzVbisDV1moLCW2moKraGYREURWBnE9XuFnv3GdPkgcm7Ub8lS7rS0cZaGylthqAq6imUVEEFloIWwbw+9Lib6OqoPZPLO4TZ5qt7WFoyxU1hJbTWA3YgSRBfr3/KvGXm8Dv99zrKY7nom20XCVhcpSYksGFV8EQfxphHudKOKclpuOv9lRghXOslChJbYk/CsmggjFlSKnvduaZbDZwj8BcJeFCimx1cS97GikCCIUSkDYvixgXrnT/SzfhlE1yioLlVZiq4m4UuocBTE7TKqDxT/nkBihFcz2HF/0IpNCvtWyydhu/nIVxOxAafDf1d59Jrp/eAcRhYIetvLMLN8wKAjdkiyaWVYEQeE4pdHX1f77UR+pg18tKkUmhZ6njg/UCkLpVKVophSZBP8BKVaEaPjSlXAAAAHbdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93PjxtaT5MPC9taT48bWk+dDwvbWk+PC9tcm93Pjxtcm93PjxtaT54PC9taT48bW8+KzwvbW8+PG1pPmE8L21pPjwvbXJvdz48L21mcmFjPjxtZnJhYz48bXJvdz48bW4+MTwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bWk+Y29zPC9taT48bW8+JiN4QTA7PC9tbz48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWk+YTwvbWk+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5iPC9taT48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5jPC9taT48L21yb3c+PC9tZmVuY2VkPjwvbXJvdz48bXJvdz48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPiYjeDNCMTs8L21pPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjwvbWF0aD5274SdAAAAAElFTkSuQmCC)
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,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)
maths-General
Maths-
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
Maths-General
maths-
maths-General