Question

If the zeroes of a polynomial p(x) are –3 and 8, then p(x) equals

Options

• x² + 5x – 4

• (x + 3)(–x + 8)

• a(x² + 5x – 24)

• x² – 24

Answer 1

(x + 3)(–x + 8)

Explanation:

Given zeroes: α = –3 and β = 8.

The factored form is:

p(x) = k(x – (–3))(x – 8)

p(x) = k(x + 3)(x – 8)

Let’s check the options:

(A) x² + 5x – 4: Sum of roots is –5. Incorrect.

(B) (x + 3)(–x + 8): Here, if we set the expression to 0, we get x + 3 = 0

⇒ x = –3 and –x + 8 = 0

⇒ x = 8

Note that this is just the form with k = –1.

(C) a(x² + 5x – 24): For this, sum of roots is –5. Incorrect.

(D) x² – 24: Roots are `± sqrt(24)`. Incorrect.

The polynomial is (x + 3)(–x + 8).