The quadratic equation x kx2 2 02 + + = has equal roots, if the value of k is:(a) – 4 (b) 2(c) ± 4 (d) 4
Question
The quadratic equation x kx2 2 02 + + = has equal roots, if the value of k is:(a) – 4 (b) 2(c) ± 4 (d) 4
Solution
The given quadratic equation is kx^2 + 2x + 2 = 0.
For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant (b^2 - 4ac) must be equal to zero.
In this case, a = k, b = 2, and c = 2.
So, we have (2)^2 - 4k2 = 0.
Solving this equation gives us:
4 - 8k = 0, 8k = 4, k = 4/8, k = 0.5.
So, none of the given options (a) -4, (b) 2, (c) ± 4, (d) 4 are correct. The value of k for which the given quadratic equation has equal roots is 0.5.
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