Maths-
General
Easy
Question
If α,β then the equation
with roots
will be
- none of these
Hint:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. Here we have to find the value of
if α,β are roots of the equation
.
The correct answer is: ![x to the power of 2 end exponent minus x minus 1 equals 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAARCAYAAADEz2IYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAYJJREFUeNpjYCAd/IfiX0B8FIhVGEbBoAFMQJwFxOdGg2LwgR+jQTC4gD0QHxwNhsEDJKF1itIw8pMaENcC8QUa28MHxNOA+CQUz4SKUez4LdCIGU5gMRCnQRsytAR7gdgPie8DFaMoh2yjRswOYkDLSAkF4klYxCcAcSS6YDIQd2BR3AyVgwFQhGjQIWCIdc9Qi5Q1QOyGRdwRKocBQM1bcSR+IhBPwdFPQca0AsS4Z6Ai5T8RGBt4B8RsWMRBYi+xafAA4j4o24XSco4KYKDcQ8uE9geP3C9cEruhTV1QC0SYCp4jJzWR6x5q2DeQkYKzz1cAjTG9QVLpDoR7aFl8vcRRfHHgKr6soZVNH7aWwACAgXIPrSt6DyzibtgqelAncBMQcwExDxCfoULxRQkYSPfQMlKCgHg2FvH56AlPFNrUFUbr0CweoAgZaPfQuvO4H1oss0CLsmoGtOEqkOA6IJbGonk5jqxGSzCQ7qFXc18QiOdCK/Zv0GEWHoZRMHgBAEoifwamcyyUAAAAnHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4tPC9tbz48bWk+eDwvbWk+PG1vPi08L21vPjxtbj4xPC9tbj48bW8+PTwvbW8+PG1uPjA8L21uPjwvbWF0aD6FWfk2AAAAAElFTkSuQmCC)
A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:
ax² + bx + c = 0
where a, b, and c are constant terms and x is the unknown variable.
Now we have given the equation as: ![x squared minus 3 x plus 1 equals 0](data:image/png;base64,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)
Here, a=1, b=−3 and c=1
Now we have the sum of roots as α+β=-(-3)/1=3
product of roots as α.β=1/1=1
Adding the terms
, we get :
![fraction numerator 1 over denominator alpha minus 2 end fraction plus fraction numerator 1 over denominator beta minus 2 end fraction
fraction numerator beta minus 2 plus alpha minus 2 over denominator left parenthesis alpha minus 2 right parenthesis left parenthesis beta minus 2 right parenthesis end fraction
fraction numerator beta plus alpha minus 4 over denominator alpha beta minus 2 alpha minus 2 beta plus 4 end fraction
N o w space u sin g space t h e space s u m space a n d space p r o d u c t s space w e space f o u n d space e a r l i e r comma space w e space g e t colon
fraction numerator 3 minus 4 over denominator 1 minus 2 left parenthesis 3 right parenthesis plus 4 end fraction
fraction numerator negative 1 over denominator 1 minus 6 plus 4 end fraction
fraction numerator negative 1 over denominator negative 1 end fraction equals 1 equals fraction numerator 1 over denominator alpha minus 2 end fraction plus fraction numerator 1 over denominator beta minus 2 end fraction
F o r space p r o d u c t comma space w e space g e t colon
fraction numerator 1 over denominator alpha minus 2 end fraction cross times fraction numerator 1 over denominator beta minus 2 end fraction
fraction numerator 1 over denominator left parenthesis alpha minus 2 right parenthesis left parenthesis beta minus 2 right parenthesis end fraction
fraction numerator 1 over denominator alpha beta minus 2 alpha minus 2 beta plus 4 end fraction
N o w space u sin g space t h e space s u m space a n d space p r o d u c t s space w e space f o u n d space e a r l i e r comma space w e space g e t colon
fraction numerator 1 over denominator 1 minus 2 left parenthesis 3 right parenthesis plus 4 end fraction
fraction numerator 1 over denominator negative 1 end fraction equals 1 equals fraction numerator 1 over denominator alpha minus 2 end fraction cross times fraction numerator 1 over denominator beta minus 2 end fraction
N o w space t h e space e q u a t i o n space w i l l space b e colon
x squared minus left parenthesis fraction numerator 1 over denominator alpha minus 2 end fraction plus fraction numerator 1 over denominator beta minus 2 end fraction right parenthesis x plus left parenthesis fraction numerator 1 over denominator alpha minus 2 end fraction cross times fraction numerator 1 over denominator beta minus 2 end fraction right parenthesis equals 0
P u t t i n g space t h e space v a l u e s space w h i c h space w e space f o u n d comma space w e space g e t colon
x squared minus left parenthesis 1 right parenthesis x plus left parenthesis negative 1 right parenthesis equals 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)
Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore, will be the equation for the roots
.
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maths-General
Maths-
Statement-I : If ![fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text then end text bold italic A plus bold italic B plus bold italic C equals bold 0](data:image/png;base64,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)
Statement-II :If ![fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text then end text A plus B minus C equals 0](data:image/png;base64,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)
Which of the above statements is true
Statement-I : If ![fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text then end text bold italic A plus bold italic B plus bold italic C equals bold 0](data:image/png;base64,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)
Statement-II :If ![fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text then end text A plus B minus C equals 0](data:image/png;base64,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)
Which of the above statements is true
Maths-General
Maths-
If x, y are rational number such that
Then
If x, y are rational number such that
Then
Maths-General
maths-
A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is -
A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is -
maths-General
maths-
There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is -
There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is -
maths-General
maths-
If a, b, c are the three natural numbers such that a + b + c is divisible by 6, then a3 + b3 + c3 must be divisible by -
If a, b, c are the three natural numbers such that a + b + c is divisible by 6, then a3 + b3 + c3 must be divisible by -
maths-General
maths-
For x
R, let [x] denote the greatest integer
x, then value of
+
+
+…+
is -
For x
R, let [x] denote the greatest integer
x, then value of
+
+
+…+
is -
maths-General
maths-
The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1
x
5, 12
y
18, z
–1
The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1
x
5, 12
y
18, z
–1
maths-General
maths-
Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -
Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -
maths-General
maths-
In how many ways can we get a sum of at most 17 by throwing six distinct dice -
In how many ways can we get a sum of at most 17 by throwing six distinct dice -
maths-General
maths-
The number of non negative integral solutions of equation 3x + y + z = 24
The number of non negative integral solutions of equation 3x + y + z = 24
maths-General