Question

Find a quadratic polynomial whose zeroes are 2 and -5.

Answer 1

It is given that the two roots of the polynomial are 2 and -5. 

Let α = 2 and β = -5 

Now, the sum of the zeroes, α + β = 2 + (-5) = -3 

Product of the zeroes, αβ = 2 × (-5) = -15 

∴ Required polynomial = x² – (α + β)x + αβ

= x² – (-3)x + 10 

= x² + 3x – 10