If the roots of the equation x^2 + 4x + k = 0 are equal, what is the value of k?

If the roots of the equation x^2 + 4x + k = 0 are equal, what is the value of k?

Step 1: Identify the equation given, which is x^2 + 4x + k = 0.
Step 2: Understand that for the roots of a quadratic equation to be equal, the discriminant must be zero.
Step 3: Recall the formula for the discriminant, which is given by D = b^2 - 4ac, where a, b, and c are the coefficients from the equation ax^2 + bx + c = 0.
Step 4: In our equation, a = 1, b = 4, and c = k.
Step 5: Substitute the values into the discriminant formula: D = 4^2 - 4*1*k.
Step 6: Simplify the expression: D = 16 - 4k.
Step 7: Set the discriminant equal to zero for the roots to be equal: 16 - 4k = 0.
Step 8: Solve for k by adding 4k to both sides: 16 = 4k.
Step 9: Divide both sides by 4 to isolate k: k = 16 / 4.
Step 10: Calculate the value: k = 4.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots; if it is zero, the roots are equal.
Quadratic Equation – A quadratic equation is in the form ax^2 + bx + c = 0, where a, b, and c are constants.