Question

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

Answer 1

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).`