Given that the equation kx^2 + 12x + k = 0, where k is a positive constant, has equal roots, find the value of k.

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}