One of the most important and conceptual question from polynomials in which we have given a equation 8x²-4 and in this given equation we have to find the zeroes of the quadratic polynomials and also need to verify the relationship between the zeroes and the coefficients

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

Let f(x)=8x²−4

= 4((√2x)²−(1)²)

=4(√2x+1)(√2x−1)

to find the zeroes, Let f(x)=0

(√2x+1)(√2x−1)=0

(√2x+1)=0 or (√2x−1)=0

x=(−1)/√2 or x=1/√2

So the zeroes of f(x) are −1/√2 and x=1/√2

Again

Sum of zeroes = −1/√2+1/√2=(−1+1)/√2=0=−b/a=(-coefficient of x)/(−coefficient of x²)Product of zeroes = −1/√2×1/√2=2−1=8−4=ac=coefficient of x2Constant term