Question

6. Find the value of a such that the quadratic
equation (a-4)X? + 2(a-4)x + 4 = 0 has equal
roots.
​

Answer 1

Answer:

For having equal roots, discriminant of the quadratic equation should be equal to zero.

Discriminant = b² - 4ac

where, b is the coefficient of x, a is the coefficient of x² and c is the constant term.

Therefore,

[2(a - 12)]² - 4(a - 12)(2) = 0  

→ 2²(a - 12)² = 8(a - 12)

→ 4(a - 12)² = 8(a - 12)

→ (a - 12)²/(a - 12) = 8/4

→ (a - 12) = 2

→ a = 12 + 2

→ a = 14.