Value of $k$ for which the quadratic polynomial $kx^2 + x + k$ has equal zeros.
- $\pm \displaystyle \frac{1}{2}$
- $\pm \displaystyle \frac{1}{3}$
- $\pm \displaystyle \frac{1}{4}$
- $\pm \displaystyle{1}$
Reveal answer
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A
Correct answer
Explanation
For equal zeros, the discriminant D = b^2 - 4ac must be 0. Here a=k, b=1, c=k. D = 1^2 - 4(k)(k) = 1 - 4k^2 = 0. 4k^2 = 1, k^2 = 1/4, k = +/- 1/2.
AI explanation
For a quadratic polynomial to have equal zeros, its discriminant must equal zero. The discriminant is found by squaring the coefficient of x and subtracting four times the product of the leading coefficient and the constant term. Applying this to the given polynomial gives 1 squared minus 4 times k times k, resulting in 1 minus 4 k squared. Setting this expression to zero and solving for k squared yields one fourth, so k is equal to plus or minus one half.