Question

8. Find m if (m - 12)x² + 2(m - 12)x+ 2 = 0 has real and equal roots.​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

(m - 12)x² + 2(m - 12)x+ 2 = 0

To Find :

Value of m

(m - 12)x² + 2(m - 12)x+ 2 = 0

We have this equation for equal and real roots:

$\sf{\boxed{ {b}^{2} - 4ac=0}}$

here,a=m-12 ,b=2(m-12) and c=2

$\sf[2 {(m - 12)]}^{2} - 4(m - 12) \times 2 = 0$

$\sf= > 4 {m}^{2} + 576 - 96m - 8m + 96 = 0$

$\sf= > 4 {m}^{2} - 104m + 672 = 0$

Taking 4 common:

$\sf= > {m}^{2} - 26m + 168 = 0$

$\sf= > m(m - 14) - 12(m - 14) = 0$

$\sf= > (m - 14)(m - 12) = 0$

$\bold{\red{m = 12 \:, 14}}$

So,the value of m will be 12 or 14.

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

(m - 12)x² + 2(m - 12)x+ 2 = 0

To Find :

Value of m

(m - 12)x² + 2(m - 12)x+ 2 = 0

We have this equation for equal and real roots:

$\sf{\boxed{ {b}^{2} - 4ac=0}}$

here,a=m-12 ,b=2(m-12) and c=2

$\sf[2 {(m - 12)]}^{2} - 4(m - 12) \times 2 = 0$

$\sf= > 4 {m}^{2} + 576 - 96m - 8m + 96 = 0$

$\sf= > 4 {m}^{2} - 104m + 672 = 0$

Taking 4 common:

$\sf= > {m}^{2} - 26m + 168 = 0$

$\sf= > m(m - 14) - 12(m - 14) = 0$

$\sf= > (m - 14)(m - 12) = 0$

$\bold{\red{m = 12 \:, 14}}$

So,the value of m will be 12 or 14.