Question

The number of quadratic polynomials having zeroes –5 and –3 is ______.

Options

• 1

• 2

• 3

• more than 3

Answer 1

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

Explanation:

Let the zeroes of the polynomial be α and β

then, α = –5 and β = –3

The general form of the polynomial with zeroes α and β is given by:

k[x² – (α + β)x + αβ], where k is any real number

= k[x² – (–5 – 3)x + (–5)(–3)]

= k[x² + 8x + 15]

Hence, more than 3 polynomials can have zeroes the –3 and –5.