Question

Find all the zeroes of the polynomial 4x^2-4x-3 and verify the relationship

Answer 1

♠ POLYNOMIALS ♠

The given quadratic polynomial is,

p(x) =4x² - 4x - 3

=> 4x² - 6x + 2x - 3

=> 2x( 2x -3) + 1(2x + 3)

=> (2x + 1) (2x -3)

p(x) = 0

(2x + 1) = 0 or (2x-3) = 0

x=-1/2 or x= 3/2

Hence, -1/2 and 3/2 are the zeroes of p(x).

Sum of zeroes = -1/2 + 3/2 = 2/2 = 1 = Coefficient of x / Coefficient of x²

Product of zeroes = (-1/2)(3/2) = -3/4 = Constant term/ Coefficient of x²

Hope this would help you!!^^