If the roots of the quadratic equation x^2 + 4x + k = 0 are equal, what is the v
Practice Questions
Q1
If the roots of the quadratic equation x^2 + 4x + k = 0 are equal, what is the value of k?
4
8
16
0
Questions & Step-by-Step Solutions
If the roots of the quadratic equation x^2 + 4x + k = 0 are equal, what is the value of k?
Step 1: Identify the quadratic equation given, which is x^2 + 4x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant is calculated using 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. Set the discriminant equal to zero: 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 (b^2 - 4ac) determines the nature of the roots of a quadratic equation. For equal roots, the discriminant must be zero.
