Write the family of quadratic polynomials having -1/4 and 1 as its zeros.

Question

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

Answer 1

Given,

– 1/4 and 1 are the zeros

So,

k[(x + 1/4)(x – 1)]

k[x² – 1x + 1/4x – 1/4]

f(x) = k[x² – 3/4 x – 1/4]

Where k is any non - zero real number.