Question

Find the zeros of the quadratic polynomials 5x² - 4 - 8x and verify the relationship between the zeros and the coefficients.

Answer 1

Let f(x) = 5x² ˗ 4 ˗ 8x

= 5x² ˗ 8x ˗ 4

= 5x² ˗ (10x ˗ 2x) ˗ 4

= 5x² ˗ 10x + 2x ˗ 4

= 5x (x ˗ 2) + 2(x ˗ 2)

= (5x + 2) (x ˗ 2)

To find the zeroes, set f(x) = 0

(5x + 2) (x ˗ 2) = 0

5x + 2 = 0 or x ˗ 2 = 0

x = (−2)/5 or x = 2

Again,

Sum of zeroes = (-2)/5 + 2 = (-2+10)/5 = 8/5

= -b/a

= (-Coefficient of x)/(Cofficient of x²)

Product of zeroes = (-2/5) x 2 = (-4)/5

= c/a

= Constant term / Coefficient of x²