What is the value of k if the equation x^2 + kx + 16 = 0 has roots that are equa
Practice Questions
Q1
What is the value of k if the equation x^2 + kx + 16 = 0 has roots that are equal?
8
16
4
0
Questions & Step-by-Step Solutions
What is the value of k if the equation x^2 + kx + 16 = 0 has roots that are equal?
Step 1: Understand that the equation is x^2 + kx + 16 = 0.
Step 2: Identify 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 of the equation ax^2 + bx + c.
Step 4: In our equation, a = 1, b = k, and c = 16.
Step 5: Substitute the values into the discriminant formula: D = k^2 - 4*1*16.
Step 6: Simplify the equation: D = k^2 - 64.
Step 7: Set the discriminant equal to zero for equal roots: k^2 - 64 = 0.
Step 8: Solve for k by adding 64 to both sides: k^2 = 64.
Step 9: Take the square root of both sides: k = ±8.
