Find the roots of the following quadratic equation by factorisation,3(

1.	Find the roots of the following quadratic equation by factorisation,3(x – 4)2 – 5(x – 4) = 12
Answer» Take (x – 4) = a, then the given Q.E. reduces to 3a² – 5a = 12 ⇒ 3a² – 5a – 12 = 0 ⇒ 3a² – 9a + 4a – 12 = 0 ⇒ 3a(a – 3) + 4(a – 3) = 0 ⇒ (a – 3) (3a + 4) = 0 ⇒ a – 3 = 0 or 3a + 4 = 0 ⇒ a = 3 or a = \(\frac{-4}{3}\) but a = x – 4 x – 4 = 3 (or) x – 4 = \(\frac{-4}{3}\) ⇒ x = 7 or x = 4 – \(\frac{-4}{3}\) = \(\frac{8}{3}\) ∴ x = 7 or \(\frac{8}{3}\) are the roots of the given Q.E.

Find the roots of the following quadratic equation by factorisation,3(x – 4)2 – 5(x – 4) = 12

Answer»

Take (x – 4) = a, then the given Q.E. reduces to

3a² – 5a = 12

⇒ 3a² – 5a – 12 = 0

⇒ 3a² – 9a + 4a – 12 = 0

⇒ 3a(a – 3) + 4(a – 3) = 0

⇒ (a – 3) (3a + 4) = 0

⇒ a – 3 = 0 or 3a + 4 = 0

⇒ a = 3 or a = \(\frac{-4}{3}\)

but a = x – 4

x – 4 = 3 (or) x – 4 = \(\frac{-4}{3}\)

⇒ x = 7 or x = 4 – \(\frac{-4}{3}\) = \(\frac{8}{3}\)

∴ x = 7 or \(\frac{8}{3}\) are the roots of the given Q.E.