Find the values o f k for which the following equation has equal roots

1.	Find the values o f k for which the following equation has equal roots.(k - 12)x2 + 2(k - 12) + 2 = 0
Answer» GivEn:- (k - 12)x² + 2(k - 12) + 2 = 0 has equal roots. To find:- Value of k SoluTion:- Here, a = (k - 12) b = 2(k - 12) c = 2 ☯ ${\underline{\underline{\bf{According\;to\;question -}}}}$ As we KNOW that, Discriminant, D = b² - 4ac ★ Putting values in above formula - D = [2(k - 12)]² - 4 × (k - 12) × 2 Roots are equal, if D = 0 $\dashrightarrow$ 4[k² + 144 - 24k] - (8k - 96) = 0 $\dashrightarrow$ 4k² + 576 - 96k - 8k + 96 = 0 $\dashrightarrow$ 4k² - 104k + 672 = 0 $\dashrightarrow$ k² - 26k + 168 = 0 $\dashrightarrow$ k² - 14k - 12k + 168 = 0 $\dashrightarrow$ k(k - 14) - 12(k - 14) = 0 $\dashrightarrow$ (k - 14)(k - 12) = 0 Here, both (k - 14) and (k - 12) are equals to 0. $\therefore$ k = 12 ,14 But k = 12 doesn't satisfy the equation. Therefore, 14 is the correct value of k for the given Equation. $\dag$ Hence, k = 14 ▬▬▬▬▬▬▬▬▬▬

Find the values o f k for which the following equation has equal roots.(k - 12)x2 + 2(k - 12) + 2 = 0

Answer»

GivEn:-

(k - 12)x² + 2(k - 12) + 2 = 0 has equal roots.

To find:-

Value of k

SoluTion:-

Here,

a = (k - 12)

b = 2(k - 12)

c = 2

☯ ${\underline{\underline{\bf{According\;to\;question -}}}}$

As we KNOW that,

Discriminant, D = b² - 4ac

★ Putting values in above formula -

D = [2(k - 12)]² - 4 × (k - 12) × 2

Roots are equal, if D = 0

$\dashrightarrow$ 4[k² + 144 - 24k] - (8k - 96) = 0

$\dashrightarrow$ 4k² + 576 - 96k - 8k + 96 = 0

$\dashrightarrow$ 4k² - 104k + 672 = 0

$\dashrightarrow$ k² - 26k + 168 = 0

$\dashrightarrow$ k² - 14k - 12k + 168 = 0

$\dashrightarrow$ k(k - 14) - 12(k - 14) = 0

$\dashrightarrow$ (k - 14)(k - 12) = 0

Here, both (k - 14) and (k - 12) are equals to 0.

$\therefore$ k = 12 ,14

But k = 12 doesn't satisfy the equation.

Therefore, 14 is the correct value of k for the given Equation.

$\dag$ Hence, k = 14