Question

Factorise p²- p - 72

Answer 1

Answer:

Hope answer will help u

Answer 2

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Question :

Factorize :

• p²-p-72=0

To find :

• The value of p =?

Solution :

Method (I)

$\large \red{ \bold{ \underline{ \underline{step \: by \: step \: explaination : }}}}$

$\\ \large \implies \bf \: {p}^{2} - p - 72 = 0$

$\\ \large\implies \tt \: {p}^{2} - p - 72 = 0$

$\\ \large \implies \tt \: {p}^{2} - 9p + 8p - 72 = 0$

$\\ \large \implies \tt \: p(p - 9) + 8(p - 9) = 0$

$\\ \large\implies \tt \: (p - 9)(p + 8) = 0$

$\\ \large \implies \tt \: p = 9 \: \: \: \: and \: \: \: \: p = - 8$

$\: \: \: \: \: \: \: \\ \red \bigstar \large\boxed{ \boxed{ \underline{ \underline{ \bf\:the \: value \: of \: p = 9}}}}$

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Method (II)

• a=1

• b=-1

•c=-72

$\bullet \pink{\bf{\underline{ \: by \: using \: determinant \: form}}}$

$\\ \implies \large \tt \: \: {b}^{2} - 4ac$

$\\ \implies \large \tt \: {( - 1)}^{2} - 4(1)( - 72)$

$\\ \implies \large \sf \: 1 + 288 = 289$

$\red {\large \bf{ \underline{by \: using \: formula \: method : }}}$

$\\ \implies \large \sf \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\\ \implies \large \sf \: x = \frac{1 \pm17}{2}$

$\\ \implies \large \sf \: x = \frac{1 + 17}{2} \: \: and \: \: x = \frac{1 - 17}{2}$

$\\ \implies \large \sf \: x = \frac{18}{2} \: \: and \: \: x = - \frac{16}{2}$

$\\ \implies \large \sf \: x = 9 \: \: and \: \: x = - 8$

$\\ \therefore \green{\bf{ \underline{roots \: of \: this \: given \: equation \: is \pink{\: x = 9 }\: \: and \: \: \pink{ x = - 8}}}}$