Question

Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:

Options

• 9, 1

• −9, 1

• 9, −1

• −9, −1

Answer 1

9, 1

Explanation:

Correct sum = 8 + 2 = 10 from Mohan

Correct product = −9 × −1 = 9 from Sohan

∴ x² – (10)x + 9 = 0

⇒ x² – 10x + 9 = 0

⇒ x² – 9x – x + 9 = 0

⇒ x(x – 9) – 1(x – 9) = 0

⇒ (x – 9) (x – 1) = 0

⇒ Correct roots are 9 and 1.