Question

If one of the zeros of the cubic polynomial x³ + ax² + bx + c is –1 then the product of the other two zeros is ______.

Options

• a – b – 1

• b – a – 1

• 1 – a + b

• 1 + a – b

Answer 1

If one of the zeros of the cubic polynomial x³ + ax² + bx + c is –1 then the product of the other two zeros is 1 – a + b.

Explanation:

Since –1 is a zero of x³ + ax² + bx + c, we have

(–1)³ + a × (–1)² + b × (–1) + c = 0

⇒ a – b + c – 1 = 0 

⇒ c = 1 – a + b

Also, product of all zeros is given by

αβ × (–1) = –c 

⇒ αβ = c

⇒ αβ = 1 – a + b