Find the value of k for which the equation x² + kx + 16 = 0 has equal roots. (20

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Question: Find the value of k for which the equation x² + kx + 16 = 0 has equal roots. (2022)

Options:

Correct Answer: -8

Solution:

For equal roots, the discriminant must be zero: k² - 4*1*16 = 0, thus k² = 64, k = ±8. The value of k can be -8.

Find the value of k for which the equation x² + kx + 16 = 0 has equal roots. (2022)

Find the value of k for which the equation x² + kx + 16 = 0 has equal roots. (2022)

Step 1: Identify the equation given, which is x² + kx + 16 = 0.
Step 2: Recall that for a quadratic equation ax² + bx + c = 0, the discriminant (D) is given by the formula D = b² - 4ac.
Step 3: In our equation, a = 1, b = k, and c = 16.
Step 4: Substitute the values into the discriminant formula: D = k² - 4*1*16.
Step 5: Simplify the expression: D = k² - 64.
Step 6: For the roots to be equal, set the discriminant equal to zero: k² - 64 = 0.
Step 7: Solve for k²: k² = 64.
Step 8: Take the square root of both sides: k = ±8.
Step 9: The possible values for k are 8 and -8. The question asks for the value of k, so we can choose -8.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots; for equal roots, it must be zero.
Quadratic Formula – The quadratic formula is used to find the roots of a quadratic equation, and the discriminant is part of this formula.