Question

Find the quadratic polynomial whose zeroes are 2 and -6. Verify the relation between the coefficients and the zeroes of the polynomial.

Answer 1

Let ∝ = 2 and β = -6

Sum of the zeroes = (∝ + β) = 2 – 6 = -4

Product of the zeroes, = 2(-6) = -12

Required quadratic polynomial is

x² – (∝+β)x + ∝β 

= x² – (-4)x – 12

= x² + 4x – 12

And,

Sum of the zeroes = – 4 = -4/1 = (-Coefficient of x)/(Cofficient of x²)

Product of zeroes = -12 = -12/1 = Constant term / Coefficient of x²