Question

Find the zeroes of the quadratic polynomial f(x) = 5x ² ˗ 4 ˗ 8x and verify the relationship between the zeroes and coefficients of the given polynomial.

Answer 1

We have: 

f(x) = 5x² ˗ 4 ˗ 8x 

 = 5x² ˗ 8x ˗ 4 

 = 5x² ˗ (10x ˗ 2x) ˗ 4 

 = 5x² ˗ 10x + 2x ˗ 4 

 = 5x (x ˗ 2) + 2(x ˗ 2) 

 = (5x + 2) (x ˗ 2) 

∴ f(x) = 0 ⇒ (5x + 2) (x ˗ 2) = 0 

 ⇒ 5x + 2= 0 or x ˗ 2 = 0 

 ⇒ x = −2/ 5 or x = 2 

So, the zeroes of f(x) are −2/ 5 and 2.