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A Quadratic Polynomial, the Sum of Whose Zeroes is 0 and One Zero is 3, is - Mathematics

MCQ

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is

Options

  • x2 − 9

  • x2 + 9

  • x2 + 3

  • x2 − 3

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Solution

Since `alpha ` and `beta` are the zeros of the quadratic polynomials such that

`0 = alpha + beta`

If one of zero is 3 then

`alpha + beta =0`

`3 + beta = 0`

`beta = 0 -3`

`beta =-3`

Substituting `beta =-3` in  `alpha + beta =0` we get

`alpha -3 =0`

`alpha =3`

Let S and P denote the sum and product of the zeros of the polynomial respectively then

`S = alpha+ beta`

`S = 0`

`P = alphabeta`

`P = 3xx-3`

` P = -9`

Hence, the required polynomials is

`= (x^2 - Sx + p)`

`= (x ^2 - 0x- 9)`

`= x^2 - 9`

Hence, the correct choice is  `(a).`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 26 | Page 64
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