Question

Factorise the following by splitting the middle term m*2 -15m+16

Answer 1

Question :-

Find factors of the following by splitting the middle term m² - 15m + 16 = 0.

Answer :-

$\to \boxed{ \sf{ m = \frac{15 + \sqrt{161} }{2} \: and \: \frac{15 - \sqrt{161} }{2} }} \:$

Explanation :-

We have

→ m² - 15m+ 16 = 0 ,...eq.(1)

Here , we should use quadratic formula for find factors , here middle term is not splitting for a simple process .

Hence, we know that the quadratic formula ,

→ If we have → ax² + bx + c = 0....eq.(2)

$\to \boxed{\sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

Compare eq.(1) with eq.(2)

We get , a = 1 , b = -15 and c = 16,

put these in quadratic formula

$\to \sf{m = \frac{ - ( - 15) \pm \sqrt{ {( - 15)}^{2} - 4 \times 16 \times 1} }{2} } \\ \\ \to \sf{m = \frac{15 \pm \sqrt{225 -64 } }{2} } \\ \\ \to \sf{ m = \frac{15 \pm \sqrt{161} }{2} } \\ \\ \to \boxed{ \sf{ m = \frac{15 + \sqrt{161} }{2} \: and \: \frac{15 - \sqrt{161} }{2} }}$

Answer 2

$\tt{\red{\huge{Hello !!! }}} S.dlD$

QUESTION :

Factorise the following by splitting the middle term m*2 -15m+16.

SOLUTION :

This can't be solved by directly Factorising..

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C,

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C, We get the following Information...

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C, We get the following Information...=> a = 1

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C, We get the following Information...=> a = 1 => b = -15

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C, We get the following Information...=> a = 1 => b = -15 => c = 16.

This can't be solved by directly Factorising..So it has to be solved using the Shridharacharya ' s Formula...Comparing with a Quadratic Equation of the form AX^2 + BX + C, We get the following Information...=> a = 1 => b = -15 => c = 16.Substituting these into the required Formulae,

=> $\begin{lgathered}\to \sf{m = \frac{ - ( - 15) \pm \sqrt{ {( - 15)}^{2} - 4 \times 16 \times 1} }{2} } \\ \\ \to \sf{m = \frac{15 \pm \sqrt{225 -64 } }{2} } \\ \\ \to \sf{ m = \frac{15 \pm \sqrt{161} }{2} } \\ \\ \to \boxed{ \sf{ m = \tt{\leadsto{\purple{\dfrac{15 + \sqrt{161} }{2}}}}}}} \: and \: \frac{15 - \sqrt{161} }{2} .(A)\end{lgathered}$