If the quadratic equation x^2 + kx + 16 = 0 has equal roots, what is the value o
Practice Questions
Q1
If the quadratic equation x^2 + kx + 16 = 0 has equal roots, what is the value of k?
-8
-4
4
8
Questions & Step-by-Step Solutions
If the quadratic equation x^2 + kx + 16 = 0 has equal roots, what is the value of k?
Step 1: Identify the quadratic equation, which is x^2 + kx + 16 = 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 = k, and c = 16.
Step 4: Substitute the values into the discriminant formula: D = k^2 - 4*1*16.
Step 5: Simplify the expression: D = k^2 - 64.
Step 6: For the roots to be equal, the discriminant must be zero: set D = 0, so k^2 - 64 = 0.
Step 7: Solve the equation k^2 - 64 = 0 by adding 64 to both sides: k^2 = 64.
Step 8: Take the square root of both sides: k = ±8.
Step 9: Since we are looking for a specific value of k, we can choose k = -8.
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.
