Question

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

Answer 1

Let f(x) = (x² – 5)

= (x²-(√5)²)

= (x + √5)(x – √5)

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

(x + √5)(x – √5)=0

x = -√5 or x = √5

Again,

Sum of zeroes = -√5 + √5 = 0/1

= -b/a

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

Product of zeroes = -√5 + √5 = -5 = -5/1

= c/a

= Constant term / Coefficient of x²