Question

x^2 + 5x+6 . find its root and verify it​

Answer 1

Equation:

==> x² + 5x + 6

==> x² + 3x + 2x + 6

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

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

Zeroes are -3 and -2

Verification:

1) Substitute x = -3

==> (-3)² + 5(-3) + 6

==> 9 - 15 + 6

==> 15 - 15

==> 0

2) Substitute x = -2

==> (-2)² + 5(-2) + 6

==> 4 - 10 + 6

==> 10 - 10

==> 0

Hence, Proved.

Answer 2

Step-by-step explanation:

Given -

p(x) = x² + 5x + 6

To Find -

• Its root and verify it

Now,

x² + 5x + 6

» x² + 2x + 3x + 6

» x(x + 2) + 3(x + 2)

» (x + 3)(x + 2)

Zeroes/Roots are -

» x + 3 = 0 and x + 2 = 0

• » x = -3 and x = -2

Verification -

As we know that :-

• α + β = -b/a

It means,

-3 + (-2) = -(5)/1

» -3 - 2 = -5

» -5 = -5

LHS = RHS

And

• αβ = c/a

It means,

» -3 × -2 = 6/1

» 6 = 6

LHS = RHS

Hence,

Verified..