For the quadratic equation x^2 + 4x + k = 0 to have equal roots, what must be th

For the quadratic equation x^2 + 4x + k = 0 to have equal roots, what must be the value of k? (2022)

For the quadratic equation x^2 + 4x + k = 0 to have equal roots, what must be the value of k? (2022)

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

Discriminant of a Quadratic Equation – The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. For the equation to have equal roots, the discriminant must be zero.
Quadratic Formula – The roots of a quadratic equation can be found using the quadratic formula x = (-b ± √D) / (2a), where D is the discriminant.