Question

solve X2+5X+6= 0 for values of X?​

Answer 1

The values of x are x=-2 and x=-3

Explanation:

Given:

x²+5x+6 =0

To find:

The roots of the equation:

Formula:

$\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Solution:

==> x²+5x+6 =0

==> a = coefficient of x²

==> b = Coefficient of x

==> c = Constant

==> a = 1

==> b = 5

==> c = 6

==> Substitute the values in the formula

==> $\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

==> $\alpha =\frac{-5+\sqrt{5^{2}-4(1)(6) } }{2(1)}$

==>  $\alpha =\frac{-5+\sqrt{25-4(6) } }{2}$

==>$\alpha =\frac{-5+\sqrt{25-24 } }{2}$

==> $\alpha =\frac{-5+\sqrt{1 } }{2}$

==> $\alpha =\frac{-5+1}{2}$

==> $\alpha =\frac{-4}{2}$

==> α= -2

==> $\beta=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

==> $\beta =\frac{-5-\sqrt{5^{2}-4(1)(6) } }{2(1)}$

==> $\beta =\frac{-5-\sqrt{25-4(6) } }{2}$

==>$\beta =\frac{-5-\sqrt{25-24 } }{2}$

==> $\beta =\frac{-5-\sqrt{1 } }{2}$

==> $\beta =\frac{-5-1}{2}$

==> $\beta =\frac{-6}{2}$

==> β= -3

The roots are α= -2 and  β= -3

We can write this as, (x+2) and (x+3)

The values of x are x=-2 and x=-3