Question

The number of polynomials having zeroes as –2 and 5 is ______.

Options

• 1

• 2

• 3

• More than 3

Answer 1

The number of polynomials having zeroes as –2 and 5 is more than 3.

Explanation:

According to the question,

The zeroes of the polynomials = –2 and 5

We know that the polynomial is of the form,

p(x) = ax² + bx + c.

Sum of the zeroes = – (Coefficient of x) ÷ Coefficient of x² i.e.

Sum of the zeroes = – `b/a`

– 2 + 5 = `– b/a`

3 = `– b/a`

b = – 3 and a = 1

Product of the zeroes = Constant term ÷ Coefficient of x² i.e.

Product of zeroes = `c/a`

(–2)5 = `c/a`

– 10 = c

Substituting the values of a, b and c in the polynomial p(x) = ax² + bx + c.

We get, x² – 3x – 10

Therefore, we can conclude that x can take any value.