The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k

₹0.0

Question: The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k?

Options:

Correct Answer: -8

Solution:

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, solving gives k = -8.

The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k?

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 the problem asks for the value of k, we can choose k = -8.

Quadratic Equations – Understanding the properties of quadratic equations, particularly the condition for equal roots which involves the discriminant.
Discriminant – The discriminant of a quadratic equation determines the nature of the roots; for equal roots, it must be zero.