Find the quadratic polynomial whose zeroes are 2 and -6. Verify the re

1.	Find the quadratic polynomial whose zeroes are 2 and -6. Verify the relation between the coefficients and the zeroes of the polynomial.
Answer» Let α = 2 and β = - 6 Sum of the zeroes, (α+ β) = 2 + (- 6) = - 4 Product of the zeroes,αβ = 2 × (-6) = -12 ∴ Required polynomial = x² - (α +β)x + αβ = x² – (- 4)x – 12 = x² + 4x – 12 Sum of the zeroes = -4 = \(\frac{-4}1\) = \(\frac{-(coefficient\,of\,x)}{(coefficient\,of\,x^2)}\) Product of zeroes = -12 = = \(\frac{-12}1\) = \(\frac{constant\,term}{(coefficient\,of\,x^2)}\)

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

Answer»

Let α = 2 and β = - 6

Sum of the zeroes, (α+ β) = 2 + (- 6) = - 4

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

∴ Required polynomial = x² - (α +β)x + αβ = x² – (- 4)x – 12

= x² + 4x – 12

Sum of the zeroes = -4 = \(\frac{-4}1\) = \(\frac{-(coefficient\,of\,x)}{(coefficient\,of\,x^2)}\)

Product of zeroes = -12 = = \(\frac{-12}1\) = \(\frac{constant\,term}{(coefficient\,of\,x^2)}\)