Math, asked by shaikharfat800, 10 months ago

find the root of the following x2+6x+7=0 quadratic equation

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Answered by badatyasujata756

not possible because 7 is prime number

Answered by Mihir1001

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$Answer:$

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$Step-by-step-explaination:$

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let, $p(x) = {x}^{2} + 6x + 7 = 0$

This equation is of the form $a {x}^{2} + bx + c = 0$ , where . a = 1 , . b = 6 and . c = 7 .

Therefore,

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

$\implies D = {(6)}^{2} - 4(1)(7)$

$\implies D = 36 - 28$

$\implies D = 8$

Thus, D > 0.

Thus, the roots of the polynomial p(x) are real and unequal.

Hence,

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

$\implies x = \frac{ - (6) \pm \sqrt{8} }{2(1)}$

$\implies x = \frac{2( - 3 \pm \sqrt{2} )}{2}$

$\implies x = - 3 \pm \sqrt{2}$

Hence,

$\huge{ x = - 3 - \sqrt{2} }$ .............or............ $\huge{ x = - 3 + \sqrt{2} }$

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