Question

Find the roots of the qe:x2+5x-50=0by the split method,factorization and formula method

Answer 1

$\huge \mathtt{ \fbox{Solution :)}}$

$\sf Given \: \begin{cases} \sf (i) \: The \: quadratic \: equation \: is \: {(x)}^{2} + 5x - 50 = 0 \\ \\ \sf (ii) \: Here \: a = 1 \: , \: b = 5 \sqrt{3} \: and \: c = -50\end{cases}$

1) By prime factorisation method

$\sf \mapsto {(x)}^{2} + 5x - 50 = 0 \\ \\ \sf \mapsto </p><p> {(x)}^{2} - 5x + 10x - 50 = 0 \\ \\ \sf \mapsto </p><p>x(x - 5) + 10(x - 5) = 0 \\ \\ \sf \mapsto </p><p>(x + 10) (x - 5) = 0 \\ \\ \sf \mapsto </p><p>x = -10 \: \: or \: \: x = 5$

2) By quadratic formula

We know that , the quadratic formula is given by ,

$\mathtt{ \large{\fbox{x = \frac{ - b± \sqrt{ {(b)}^{2} - 4ac} }{2a} }}}$

Substitute the known values , we get

$\sf \mapsto x = \frac{ - 5 ±\sqrt{ {(5)}^{2} - 4(1)( - 50) } }{2(1)} \\ \\ \sf \mapsto x = \frac{ - 5± \sqrt{25 + 200} }{2} \\ \\ \sf \mapsto x = \frac{ - 5±15}{2} \\ \\ \sf \mapsto x = \frac{ - 5 - 15}{2} \: \: or \: \: \frac{ - 5 + 15}{2} \\ \\ \sf \mapsto x = - 10 \: \: or \: \: x = 5$

Hence , the roots of given quadratic equation are 5 and - 10

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