Multiple choice

For what values of c in the equation 2x2 – (c3 + 8c – 1)x + c2 – 4c = 0 the roots of the equation would be opposite in signs?

  1. c Ɛ (0, 4)

  2. c Ɛ (- 4, 0)

  3. c Ɛ (0, 3)

  4. c Ɛ (- 4, 4)
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A Correct answer
Explanation

For roots to have opposite signs, their product must be negative. The product is (c^2 - 4c)/2, so c(c - 4) < 0, which holds for 0 < c < 4.

AI explanation

For the quadratic equation two x squared minus the quantity of c cubed plus eight c minus one times x plus c squared minus four c equals zero, the product of the roots is given by c squared minus four c divided by two. For the roots to be opposite in signs, their product must be negative, so we set c squared minus four c divided by two to be less than zero. Multiplying by two and factoring the quadratic inequality yields c times the quantity of c minus four being less than zero, which means c must lie between zero and four.

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