Question

Find the zeroes of the polynomial f(x) = x² – 2x – 8 and verify the relation between its zeroes and coefficients.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

x² – 2x – 8

Answer 1

x² – 2x – 8 = 0

⇒ x² – 4x + 2x – 8 = 0

⇒ x(x – 4) + 2(x – 4) = 0

⇒ (x – 4) (x + 2) = 0

⇒ (x – 4) = 0 or (x + 2) = 0

⇒ x = 4 or x = –2

Sum of zeroes = 4 + (–2)

= 2

= `2/1`

= `(-("Coefficient of"  x))/(("Coefficent of"  x^2))` 

Product of zeroes = (4) (–2)

= `(-8)/1`

= `("Constant term")/(("Coefficient of"  x^2))`