Question

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

4, 1

Answer 1

Given: α + β = 4, αβ = 1

α + β = `(-b)/a = 4/1` and αβ = `c/a = 1`

By comparison a = 1, b = -4 and c = 1

Hence, after substituting the values in ax² + bx + c,

ax² + bx + c = (1)x² + (-4)x + 1

= x² – 4x + 1

Hence, the quadratic polynomial is x² – 4x + 1.