Question

Factorize 3m^2-10m+8​

Answer 1

Solution:-

Method:-1

Given equation

$\rm \implies3 {m}^{2} - 10m + 8$

Split into middle terms , we get

$\rm \implies3 {m}^{2} - 6m - 4m + 8 = 0$

$\rm \implies3m(m - 2) - 4(m - 2) = 0$

$\rm \implies \: (3m - 4)(m - 2) = 0$

$\rm \implies3m - 4 = 0 \: \: and \: \: m - 2 = 0$

$\rm \implies m = \dfrac{4}{3} \: \: and \: m = 2$

Method:- 2

Using quadratic formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

we have equation

$\rm \implies3 {m}^{2} - 10m + 8$

Compare with

$\implies \rm \: a {m}^{2} + bm + c$

So we get

$\rm \implies \: a = 3,b = - 10 \: and \: c = 8$

Put the value on formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

$\rm \implies \: m \: = \dfrac{ - ( - 10) \pm \sqrt{( - 10)^{2} - 4 \times 3 \times 8} }{2 \times 3}$

$\rm \implies \: m = \dfrac{10 \pm \sqrt{100 - 96} }{6}$

$\rm \implies \: m = \dfrac{10 \pm \sqrt{4} }{6}$

$\rm \implies \: m = \dfrac{10 + 2}{6} \: and \: m \: = \dfrac{10 - 2}{6}$

$\rm \implies \: m = \dfrac{12}{6} \: and \: m = \dfrac{8}{6}$

$\rm \implies \: m \: = 2 \: \: and \: m \: = \dfrac{4}{3}$