Multiple choice

State whether true or false. In the following quadratic equation, check the value of $k$ for which the given value is a solution of the equation or not. $k{ x }^{ 2 }+2x-3=0,x=2, is\, k=-\dfrac{1}{4}$

  1. True

  2. False
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A Correct answer
Explanation

Substitute x = 2 into the equation k(x^2) + 2x - 3 = 0. This gives k(2^2) + 2(2) - 3 = 0, which simplifies to 4k + 4 - 3 = 0, or 4k + 1 = 0. Solving for k yields k = -1/4.

AI explanation

To verify the given value, substitute x = 2 and k = -1/4 into the equation kx^2 + 2x - 3 = 0. Applying these values gives (-1/4)(2)^2 + 2(2) - 3 = 0, which simplifies to -1 + 4 - 3 = 0. Since the left-hand side evaluates to 0, satisfying the equation, the statement is true.

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