Question

Find a quadratic polynomial with zeroes -2 and 1/3.

Answer 1

Let the quadratic polynomial be ax² + bx + c, a ≠ 0 and its zeroes be α and β. 

Here α = – 2 and β = 1/3

Sum of the zeroes = α + β 

= -2 + 1/3 = -5/3

Product of the zeroes = αβ 

= 1/3 × (-2) = -2/3

∴ ax² + bx + c is [x² – (α + β)x + αβ]

= [ x² - (-5/3) x + (-2/3)]

the quadratic polynomial will be 3x² + 5x – 2.