Step 1: Know about the discrimination( b^2-4ac ) of the quadratic equation.

The discriminant indicates whether there are two, one, or no solutions.

  1) b^2 - 4ac > 0 (Positive), there are 2 real solutions

  2) b^2-4ac = 0 (Zero), there is one real solution

  3) b^2-4ac < 0 (Negative), there are 2 complex solutions or no real roots.

Step 2: Understand the given question

Quadratic equation:   kx^2 + 12x + k = 0

Constant k = ?

Quadratic equation has two equal roots

Step 3: Choose the discrimination( b^2-4ac ) of the equation.

Quadratic equation has two equal roots means one real solution

Therefore, quadratic equation discrimination, D = 0

b^2 - 4ac = 0

Step 4: Calculating the constant(k) value

Comparing the provided equation to the standard quadratic equation   ax^2 + bx + c

a = k, b = 12, and c = k

b^2 - 4ac = 0

(12)^2 - 4 (k)(k) = 0

4 k^2 = (12)^2   

k = \sqrt{\frac{(12)^2}{4}}   

k = \frac{12}{2}

k = 6

Hence, value of k = 6 , and quadratic equation 6x^2 + 12x + 6 = 0

Similar Example:

2x^2 - 3x - (k+1)

Compare it with the standard form ax^2 + bx + c      

Where a = 2, b = -3 and c = -(k+1)

HINT: Has no real root

So we have to take the discrimination of b^2-4ac < 0

Substitute all the values of a, b and c in the suitable discrimination.

[math] (-3)^2 - 4 [2][-(k+1)] < 0[/math]

  9 + 8k + 8 <0   

8k+17<0

k\ <\ \frac{-17}{8}