question 4
question 4
Correct Answer
Step-by-Step Solution
To find the value of k for which the quadratic equation 9x^2 + 8kx + 16 = 0 has real and equal roots, we use the discriminant condition. For real and equal roots, the discriminant (b^2 - 4ac) must be zero.
The given quadratic equation is in the form ax^2 + bx + c = 0, where a = 9, b = 8k, and c = 16.
The discriminant is b^2 - 4ac.
Substitute the values: (8k)^2 - 4(9)(16) = 0
Simplify: 64k^2 - 576 = 0
Add 576 to both sides: 64k^2 = 576
Divide both sides by 64: k^2 = 9
Take the square root of both sides: k = ±3
The possible values of k are 3 and -3.
Checking the options, the correct value of k is 3.
Explanation
The condition for a quadratic equation to have real and equal roots is that its discriminant must be zero. By applying this condition and solving for k, we find that k can be either 3 or -3. The correct option provided in the question is 3.
Important Formula
b^2 - 4ac = 0
Final Answer
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