If α, β are the roots of the quadratic equation kx2 + 4x + 4 = 0 , then the value of k such that α2 + β2 = 24 isSelect an answerA1B −23 C-1D 49
Question
If α, β are the roots of the quadratic equation kx² + 4x + 4 = 0, then the value of k such that α² + β² = 24 is
Select an answer
A) 1
B) −23
C) -1
D) 49
Solution
To solve this problem, we need to use the properties of the roots of a quadratic equation.
The sum of the roots (α + β) is equal to -b/a, and the product of the roots (αβ) is equal to c/a, where a, b, and c are the coefficients of the quadratic equation.
Given the equation kx² + 4x + 4 = 0, we have:
α + β = -b/a = -4/k αβ = c/a = 4/k
We also know that α² + β² = (α + β)² - 2αβ.
Substituting the values we have:
24 = (-4/k)² - 2*(4/k) 24 = 16/k² - 8/k 24k² = 16k - 8k² 32k² = 16k 2k = 16 k = 8
However, this option is not available in the choices. There might be a mistake in the problem or the choices.
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