Question

If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, then ______.

Options

• c and a have opposite signs

• c and b have opposite signs

• c and a have the same sign

• c and b have the same sign

Answer 1

If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, then c and a have the same sign.

Explanation:

The zeroes of the given quadratic polynomial ax² + bx + c where c ≠ 0, are equal.

If coefficient of x² and constant term have the same sign i.e. c and a have the same sign.

While b i.e., coefficient of x can be positive or negative but not zero.

Consider,

(i) x² + 4x + 4 = 0

${\displaystyle \Rightarrow }$ (x + 2)² = 0

${\displaystyle \Rightarrow }$ x = –2, –2 

(ii) x² – 4x + 4 = 0

${\displaystyle \Rightarrow }$ (x – 2)² = 0

${\displaystyle \Rightarrow }$ x = 2, 2