Multiple choice

Say true or false: The quadratic polynomial $x^2 + kx + k$ have equal zeroes for some odd integer $ k > 1.$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal zeroes, discriminant D = k^2 - 4k = 0. So k(k-4) = 0. k=0 or k=4. Neither 0 nor 4 is an odd integer > 1.

AI explanation

For a quadratic polynomial to have equal zeroes, its discriminant (b^2 - 4ac) must be zero. Setting the discriminant of x^2 + kx + k to zero gives k^2 - 4k = 0. This factors to k(k - 4) = 0, meaning k can only be 0 or 4. Since 4 is an even number, there is no odd integer k > 1 that makes the zeroes equal. The statement is false.

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