Question

find the value of k such that equation (k-12)x square +(k-12)x+2=0 has equal roots

Answer 1

Answer:

k = 12 or 20

Step-by-step explanation:

Given:

• Quadratic equation = (k - 12)x² + (k - 12)x + 2 = 0

To find:

The value of k = ?

Solution:

Compare the given quadratic equation with the general form of quadratic equation i.e. ax² + bx + c

We observe that:

• a = (k - 12)
• b = (k - 12)
• c = 2

When the roots are given as equal,

D = 0

⇒ b² - 4ac = 0

⇒ (k - 12)² - 4(k - 12)2 = 0

⇒ (k - 12)² = 4(k - 12)2

⇒ k² + 144 - 24k = 8k - 96

⇒ k² + 144 + 96 = 8k + 24k

⇒ k² + 240 = 32k

⇒ k² - 32k + 240 = 0

⇒ k² - 20k - 12k + 240 = 0

⇒ k (k - 20) - 12 (k - 20) = 0

⇒ (k - 12) (k - 20) = 0

∴ The value of k is 12 or 20