Multiple choice

Which of the following quadratic equations has the same roots, but has the opposite sign to the roots of 2X2 - 7X + 3 = 0?

  1. 3X2 - 7X + 2 = 0

  2. 2X2 + 7X + 3 = 0

  3. 2X2 - 7X - 2 = 0

  4. 3X2 + 7X - 2 = 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the roots of 2x^2 - 7x + 3 = 0 are alpha and beta, the roots of the new equation are -alpha and -beta. Replacing x with -x in the original equation gives 2(-x)^2 - 7(-x) + 3 = 0, which is 2x^2 + 7x + 3 = 0.

AI explanation

To find an equation with the opposite roots, we substitute -X for X in the original equation 2X^2 - 7X + 3 = 0. This gives 2(-X)^2 - 7(-X) + 3 = 0, which simplifies to 2X^2 + 7X + 3 = 0. This new equation has roots with the same magnitude but opposite signs as the original equation.

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