Question

Q.4 The root of quadratic equation x2 + 5x + 6 = 0 are
(A) 2,3
(B) -2,3
(C)2,-3
(D) -2,-3​

Answer 1

Given,

A quadratic equation, p(x) = x2 + 5x + 6 = 0

To find,

The roots of p(x).

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If (x+a) and (x+b) are two factors of a quadratic equation p(x), then (-a) and (-b) are two roots of the given quadratic equation. {Equation-1}

On factorizing the given quadratic equation, we get;

p(x) = x2 + 5x + 6 = 0

= x2 + 2x + 3x + 6 = 0

= x(x+2) + 3(x+2)

= (x+2)(x+3)

This implies,

(x+2) and (x+3) are two factors of p(x)

=> -2 and -3 are the two roots of p(x)

{by using equation-1}

Hence, -2 and -3 are the two roots of p(x) = x2 + 5x + 6.