Question

Solve the above question please.
From Class 10th Quadratic Equation ​

Answer 1

Answer:

                               k= 12 , 14  

Step-by-step explanation:

★Given:-

  The Quadratic Equation (k-12) x²+2(k-12) x+ 2=0 has Equal Roots.

★To Find:-

  The Value of k.

★Formula Applied:-

When Roots of Equation ax²+bx+c are Equal then Discriminant (b²-4ac)=0.

★Solution:-

  b²-4ac=0 where a=(k-12), b=2(k-12) and c=2.

⇒ [2k-24)]²-4×(k-12)×(2)=0

⇒ 4k²-96k+576-8k+96=0

⇒ 4k²-104k+672=0

⇒ 4(k²-26k+168)=0

⇒ k²-26k+168=$\frac{0}{4}$

⇒ k²-26k+168=0

⇒ k²-14k-12k+168=0

⇒ k(k-14)-12(k-14)=0

⇒ (k-12)(k-14)=0

$\implies \large\boxed {k=\:12\:,\:14}$