Question

Find the zeroes of the quadratic polynomial (8x² ˗ 4) and verify the relation between the zeroes and the coefficients.

Answer 1

We have: 

f(x) = 8x² ˗ 4 

It can be written as 8x² + 0x ˗ 4 

= 4 { (√2x)² ˗ (1)² } 

 = 4 (√2x + 1) (√2x ˗ 1) 

 ∴ 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 1/√2 

Here the coefficient of x is 0 and the coefficient of x² is √2