Question

For what value of a the quadratic equation 9x2-3ax+1=0 has an equal roots

Answer 1

Step-by-step explanation:

Given, 9x2 – 3kx + k = 0

For equal roots, the value of discriminant should be zero i.e.,

D = b2 – 4ac = 0

Here, a = 9, b = -3k, c = k

⇒ D = (-3k)2 – 4(9)(k) = 0

⇒ 9k2 – 36k = 0

⇒ k2 – 4k = 0

⸫ k (k – 4) = 0

⸫ k = 0 or k = 4

Answer 2

If the equation has equal roots,

so the discriminant will be equal to zero.

D=0

b^2-4ac=0

(-3a)^2-4×9×1=0

9a^2-36=0

9a^2=36

a^2=4

Therefore, a= 2 or (-2)