Question
If – 9 is a root of the equation
then the other two roots are
- 2, 7
- – 2, 7
- 2, –7
- – 2, –7
The correct answer is: 2, 7
,
by ![R subscript 1 end subscript rightwards arrow R subscript 1 end subscript plus R subscript 2 end subscript plus R subscript 3 end subscript](data:image/png;base64,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)
![left parenthesis x plus 9 right parenthesis left curly bracket left parenthesis x to the power of 2 end exponent minus 12 right parenthesis minus left parenthesis 2 x minus 14 right parenthesis plus left parenthesis 12 minus 7 x right parenthesis right curly bracket equals 0](data:image/png;base64,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)
![left parenthesis x plus 9 right parenthesis left parenthesis x to the power of 2 end exponent minus 9 x plus 14 right parenthesis equals 0](data:image/png;base64,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)
![rightwards double arrow left parenthesis x plus 9 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 7 right parenthesis equals 0](data:image/png;base64,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)
Hence the other two roots are
.
Related Questions to study
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
In the expansion of
the coefficient of
will be
In the expansion of
the coefficient of
will be
The value of
is equal to
The value of
is equal to
The sum to infinity of the given series
is
The sum to infinity of the given series
is
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
The sum of the series![fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals](data:image/png;base64,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)
The sum of the series![fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals](data:image/png;base64,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)
White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?
White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?
Which of the following is less general in characters as compared to genus?
Which of the following is less general in characters as compared to genus?
For which of the following motions gravity is not responsible?
For which of the following motions gravity is not responsible?
The velocity-time graph of a uniformly decelerating motion is a ____.
The velocity-time graph of a uniformly decelerating motion is a ____.
Sepia is also known as
Sepia is also known as
The sum of 730 + 450 using front – end estimation is______.
Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.
The sum of 730 + 450 using front – end estimation is______.
Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.
Round the number 5432 to the nearest hundred.
For rounding off to the nearest hundred, we can also look at the number formed by the tens place digit and one place digit. If the number formed is less than 50,we round down and if the number is 50 or more we round up.
Round the number 5432 to the nearest hundred.
For rounding off to the nearest hundred, we can also look at the number formed by the tens place digit and one place digit. If the number formed is less than 50,we round down and if the number is 50 or more we round up.