Question

Find the zeroes of the quadratic polynomial x² – x – 30 and verify the relation between the zeroes and its coefficients.

Answer 1

Given quadratic polynomial = x² – x – 30

⇒ x² – x – 30 = 0 = 0 

x² – 6x + 5x – 30 = 0 

⇒ x(x – 6) + 5(x – 6) = 0 

⇒ (x – 6) (x + 5) = 0 

⇒ x – 6 = 0 

x = 6 

x + 5 = 0 x = -5 

∴ Zeroes are α = 6 and β = – 5 

Sum of zeroes = α + β = \(\frac{-b}{a}\)

⇒ 6 – 5 = \(\frac{-(-1)}{1}\)

⇒ 1 = 1 

Product of zeroes α + β = 6(-5) = \(\frac{c}{a}\)

= -30 = \(\frac{-30}{1}\)

Hence the relation was verified.