We are asked to find the discriminant of a quadratic equation of the form ax^2 + bx+ c, where in this case, the equation is x^2 + 12x + 36.
First of all, for the given quadratic equation, the values of a (coefficient of x^2), b (coefficient of x) and c (constant term) are as follows:
a = 1
b = 12
c = 36
The formula to calculate the discriminant,D, of a quadratic equation is D = b^2 - 4ac.
Now, we can substitute the values of a,b and c into the discriminant formula:
D = (12)^2 - 4*1*36 = 144 - 144 = 0
Hence, the discriminant of the given equation is 0.
Remember, the value of the discriminant can tell us about the roots of the quadratic equation:
- If the discriminant is greater than 0, the quadratic equation has two distinct real roots.
- If the discriminant is equal to 0 (as in this case), the equation has exactly one real root (also known as a repeated real root).
- If the discriminant is less than 0, the roots are complex and not real.