Question

Find the zeroes of the quadratic polynomial (3x² ˗ x ˗ 4) and verify the relation between the zeroes and the coefficients.

Answer 1

3x² ˗ x ˗ 4 = 0 

⇒3x² ˗ 4x + 3x ˗ 4 = 0 

⇒x (3x ˗ 4) + 1 (3x ˗ 4) = 0 

⇒(3x ˗ 4) (x + 1) = 0 

⇒ (3x ˗ 4) or (x + 1) = 0

⇒ x = \(\frac{4}3\) or x = -1

Sum of zeroes = \(\frac{4}3\) + (-1) = \(\frac{1}3\) = \(\frac{-(coefficient\,of\,x)}{(coefficient\,of\,x^2)}\)

Product of zeroes = \(\frac{4}3\) x (-1) = \(\frac{-4}3\) = \(\frac{constant\,term}{(coefficient\,of\,x^2)}\)