Question

Solve using formula.
i. x² + 6x +5 = 0​

Answer 1

Step-by-step explanation:

We have,

$\sf{\boxed{\sf{x^{2}+6x+5=0}}\:\: .......(i)}$

From equation (i) we have,

$\sf{a=1,\: b=6\:\& \: c=5}$

Therefore,

Discriminant, $\sf{D=b^{2}-4ac}$

$\implies{\sf{D=(6)^{2}-4\times{1}\times{5}}}$

$\implies{\sf{D=36-20}}$

$\implies{\boxed{\sf{D=16}}}$

Since D>0,

Therefore, roots of the equation are given by,

$\sf{x=\frac{-b\pm\sqrt{D}}{2a}}$

$\implies{\sf{x=\frac{-6\pm\sqrt{16}}{2\times{1}}}}$

$\implies{\sf{x=\frac{-6\pm{4}}{2}}}$

$\implies{\sf{x=\frac{-6+4}{2}\:Or\:\frac{-6-4}{2}}}$

$\implies{\sf{x=\frac{-2}{2}\:Or\:\frac{-10}{2}}}$

$\implies{\sf{\boxed{\sf{x=-1}}\:Or\:\boxed{\sf{x=-5}}}}$

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