For what value of k will the quadratic equation 

(k − 12)x² + 2(k −12)x + 2 = 0 have equal roots?

The given equation is (k − 12)x² + 2(k −12)x + 2 = 0 

Comparing the equation with the general form ax² + bx + c = 0, a = k − 12, b = 2(k − 12), c = 2 

Discriminant, b² − 4ac = 4(k − 12)²− 4(k − 12) × 2  

= 4(k − 12)(k − 12 − 2)  

= 4(k − 12)(k − 14) 

For equal and real roots, D = 0

⇒ 4(k − 12)(k − 14) = 0 

⇒ k − 12 = 0 or k − 14 = 0 

⇒ k = 12 or k = 14 

However, if k = 12, then the quadratic equation does not exist. 

Thus, for k = 14, the equation will have equal roots.