The sum of the zeros of x² − 7x + 12 is ______.

The sum of the zeros of $x^{2} - 7 x + 12$ is ______.

Class 9PolynomialsPolynomials

Zeros are 3 and 4; sum = 3 + 4 = 7 (equal to −(coefficient of

x

) for a monic quadratic).

Answer: D) 7

**Linear**: ax +

b = 0

→

x = - b / a

. One zero.

Example:

3 x - 12 = 0

→

x = 4

.

**Quadratic**: solve by factorisation, or quadratic formula (Class 10).

Example:

x^{2} - 5 x + 6 = 0

. Factor:

(x - 2) (x - 3) = 0

→

x = 2

x = 3

. Two zeros.

**General principle**: a polynomial of degree n has AT MOST n real zeros.

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