Question

Find m, if the quadratic equation (m-12)x²+2(m-12)x+2=0 has real and equal roots
Please solve.
I will add the answerer in brainlist​

Answer 1

Step-by-step explanation:

Given:-

• A quadratic equation (m - 12)x² + 2(m - 12)x + 2 = 0

• The roots are real and equal.

To Find:-

• The value of m

Solution:-

For a quadratic equation ax² + bx + c = 0

If roots are real and equal → b² - 4ac = 0

In equation (m - 12)x² + 2(m - 12)x + 2 = 0

• a = coefficient of x² = (m - 12)

• b = coefficient of x = 2(m - 12)

• c = constant term = 2

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

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

$\dashrightarrow \sf {2}^{2} \times (m - 12) ^{2} = 4 \times (m - 12) \times 2$

$\dashrightarrow \sf \cancel4 \times (m - 12) ^{2} = \cancel4 \times (m - 12) \times 2$

$\dashrightarrow \sf (m - 12) ^{2} = 2(m - 12)$

$\dashrightarrow \sf {m}^{2} + 144 -( 2 \times m \times 12 )= 2m - 24$

$\dashrightarrow \sf {m}^{2} + 144 -24m= 2m - 24$

$\dashrightarrow \sf {m}^{2} + 144 -24m - 2m + 24 = 0$

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

$\dashrightarrow \sf {m}^{2} -14m - 12m + 168 = 0$

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

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

$\dashrightarrow \sf m -12 \: = 0 \: \: \: \: (or) \: \: \: m -14= 0$

$\dashrightarrow \sf m = 12\: \: \: \: \: (or) \: \: \: m = 14$

$\dashrightarrow \underline{ \boxed{ \purple{\sf \therefore \textsf{ \textbf{ m = 12 \: , 14}}}}}$

Answer 2

Step-by-step explanation:

Given:-

• A quadratic equation (m - 12)x² + 2(m - 12)x + 2 = 0

• The roots are real and equal.

${ { {\sf \ \textsf{ \textbf{ To find}}}}}\dashrightarrow</p><p>$

• The value of m

${ { \purple{\sf \ \textsf{ \textbf{ Solution}}}}}\dashrightarrow$

For a quaratic equation ax² + bx + c = 0

If roots are real and equal → b² - 4ac = 0

In equation (m - 12)x² + 2(m - 12)x + 2 = 0

• a = coefficient of x² = (m - 12)

• b = coefficient of x = 2(m - 12)

• c = constant term = 2

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

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

$\dashrightarrow \sf {2}^{2} \times (m - 12) ^{2} = 4 \times (m - 12) \times 2$

$\dashrightarrow \sf \cancel4 \times (m - 12) ^{2} = \cancel4 \times (m - 12) \times 2</p><p>$

$\dashrightarrow \sf (m - 12) ^{2} = 2(m - 12)$

$\dashrightarrow \sf {m}^{2} + 144 -( 2 \times m \times 12 )= 2m - 24</p><p>$

$\dashrightarrow \sf {m}^{2} + 144 -24m= 2m - 24$

$\dashrightarrow \sf {m}^{2} + 144 -24m - 2m + 24 = 0$

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

$\dashrightarrow \sf {m}^{2} -14m - 12m + 168 = 0$

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

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

$\dashrightarrow \sf m -12 \: = 0 \: \: \: \: (or) \: \: \: m -14= 0$

$\dashrightarrow \sf m = 12\: \: \: \: \: (or) \: \: \: m = 14$

$\dashrightarrow \underline{ \boxed{ \red{\sf \therefore \textsf{ \textbf{ m = 12 \: , 14}}}}}</p><p> </p><p> </p><p>$