Question

Find the vaule of alpha for which the equation

$( \alpha - 12)x {}^{2} + 2( \alpha - 12)x +2 = 0$

has equal roots.

Answer 1

(α - 12)x²  + 2(α - 12)x + 2 = 0

For the equation to have equal roots:

⇒ The discriminant must be equal to zero

⇒  b² - 4ac = 0

Solve α:

[2(α - 12)]²  - 4(α - 12)(2) = 0

4(α - 12)²  - 4(α - 12)(2) = 0

(α - 12)²  - (α - 12)(2) = 0

α² - 24α + 144 - 2α + 24 = 0

α² - 26α + 168 = 0

(α - 12) (α - 14) = 0

α = 12 or α = 14

Answer: α = 12 or α = 14

Answer 2

Hey there !!


▶ The given equation :-

→ (α - 12)x²  + 2(α - 12)x + 2 = 0


→ And, the equation has equal roots .



▶ To find :-

→ The value of α .


▶ Solution :-

We have,

(α - 12)x²  + 2(α - 12)x + 2 = 0

Comparing it with ax² + bx + c = 0, we get

a = α - 12 , b = 2( α - 12 ) and c = 2 .

▶ Now,

°•° D = b² - 4ac .

The equation has equal roots .

So, D = 0.

=> [2(α - 12)]²  - 4(α - 12)(2) = 0

=> 4(α - 12)²  - 4(α - 12)(2) = 0

=> (α - 12)²  - (α - 12)(2) = 0

=> α² - 24α + 144 - 2α + 24 = 0

=> α² - 26α + 168 = 0

=> (α - 12) (α - 14) = 0

•°• α = 12 or α = 14



✔✔ Hence, it is solved ✅✅.



THANKS



#BeBrainly.