Multiple choice

If the product of the roots of the equation αx2 + 6x + α2 + 1 = 0 is - 2, then a is equal to

  1. -1

  2. 1

  3. 2

  4. -2

  5. 0
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A Correct answer
Explanation

The product of the roots is (alpha^2 + 1)/alpha. Setting this equal to -2 gives alpha^2 + 1 = -2alpha, so (alpha + 1)^2 = 0. Hence, alpha = -1.

AI explanation

The formula for the product of the roots of a quadratic equation states that the product equals the constant term divided by the leading coefficient, giving (a squared + 1) / a = -2. Multiplying by a gives the quadratic equation a squared + 1 = -2a, which rearranges to a squared + 2a + 1 = 0. Factoring this perfect square yields (a + 1) squared = 0, so a is -1.

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