For what values of ‘a’ the quadratic equation 9x² – 3ax + 1 = 0 has equal roots?

OR

If one root of the quadratic equation 2x² + 2x + k = 0 is , then find the value of k.

Given: Equation 9x² – 3ax + 1 = 0 has equal roots

To find: Value of a

Concept used:

If b² – 4ac = 0 then roots of the quadratic equation ax² + bx + c = 0 are equal

Since the roots are equal,

b² – 4ac = 0 …(i)

Here, a = 9, b = -3a and c = 1

Putting the values in eq. (i), we get

(-3a)² – 4(9)(1) = 0

⇒ 9a² – 36 = 0

⇒ 9a² = 36

⇒ a² = 4

⇒ a = √4

⇒ a = ±2

Hence, the value of a is -2 and 2

OR

Given: Equation is 2x² + 2x + k = 0

To find: the value of k

Proof: One root is given it means it satisfies the given equation

2x² + 2x + k = 0

Hence, the value of k is