This is the basic and exam oriented question from polynomials in which we have given a equation x²-5 and we have been asked to find the zeroes of the given quadratic polynomials and also asked to verify the relationship between the zeroes and the coefficients

RS Aggarwal, Class 10, chapter 2A, question no 9

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