Question

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

पर्याय

• x² − 9

• x² + 9

• x² + 3

• x² − 3

Answer 1

Since ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ are the zeros of the quadratic polynomials such that

${\displaystyle 0=\alpha +\beta }$

If one of zero is 3 then

${\displaystyle \alpha +\beta =0}$

${\displaystyle 3+\beta =0}$

${\displaystyle \beta =0-3}$

${\displaystyle \beta =-3}$

Substituting ${\displaystyle \beta =-3}$ in  ${\displaystyle \alpha +\beta =0}$ we get

${\displaystyle \alpha -3=0}$

${\displaystyle \alpha =3}$

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

${\displaystyle S=\alpha +\beta }$

${\displaystyle S=0}$

${\displaystyle P=\alpha \beta }$

${\displaystyle P=3\times -3}$

${\displaystyle P=-9}$

Hence, the required polynomials is

${\displaystyle =(x^2-Sx+p)}$

${\displaystyle =(x^2-0x-9)}$

${\displaystyle =x^2-9}$

Hence, the correct choice is  ${\displaystyle \left(a\right).}$