Question

Write the family of quadratic polynomials having \[- \frac{1}{4}\] and 1 as its zeros.

Answer 1

We know that, if `x=a` is a zero of a polynomial then `x-2` is a factor of quadratic polynomials.

Since `(-1)/4`and 1 are zeros of polynomial.

Therefore `(x+1/4)(x - 1)`

`= x^2 + 1/4x-x - 1/4`

`= x^2+ 1/2 x -(1xx4)/(1xx4)x-1/4`

`= x^2 +(1-4)/4x -1/4`

`= x^2-3/4x-1/4`

Hence, the family of quadratic polynomials is `f(x)= k(x^2-3/4x-1/4)`, where k is any non-zero real number.