If the equation;
(3x)² + {27 × (3)^1/k - 15}x + 4 = 0
has equal roots find k

Step-by-step explanation:

Given quadratic equation is

can be rewritten as

Concept Used :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

Let's Solve this problem now!!!

On comparing with quadratic equation ax² + bx + c = 0, we get

Since, Discriminant, D = 0

Case - 1

So, option (b) is Correct.

Case - 2

which is not possible.

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