Question

Find the quadratic polynomial whose zeroes are `2/3` and `(-1)/4`. Verify the relation between the coefficients and the zeroes of the polynomial.

Answer 1

Let `α = 2/3` and `β = (-1)/4`

Sum of the zeroes = (α + β)

= `2/3 + ((-1)/4)` 

= `5/12`

Product of the zeroes = αβ

= `2/3 xx ((-1)/4)` 

= `(-1)/6`

Required quadratic polynomial is

x² – (α + β)x + αβ

= `x^2 - (5/12)x - ((-1)/6)`

= `1/12 (12x^2 - 5x - 2)` 

Sum of the zeroes = `5/12 = (-("Coefficient of"  x))/(("Coefficient of "x^2))` 

Product of zeroes = `(-1)/6 = ("Constant term")/("Coefficient of"  x^2)`