Multiple choice

If the roots of a quadratic equation are m + n and m – n, then the quadratic equation will be:

  1. x2 + 2mx + m2 – mn + n2 = 0

  2. x2 + 2mx + (m – n)2 = 0

  3. x2 - 2mx + m2 – n2 = 0

  4. x2 - 2mx + m2 – n2 = 1
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C Correct answer
Explanation

If the roots are m+n and m-n, the sum of roots is (m+n) + (m-n) = 2m, and the product of roots is (m+n)(m-n) = m^2 - n^2. The quadratic equation is x^2 - (sum)x + (product) = 0, which results in x^2 - 2mx + m^2 - n^2 = 0.

AI explanation

For a quadratic equation with roots m+n and m-n, the sum of the roots is (m+n) + (m-n) = 2m, and the product of the roots is (m+n)(m-n) = m^2 - n^2. The standard form of a quadratic equation is x^2 - (sum of roots)x + (product of roots) = 0. Substituting the calculated sum and product gives the equation x^2 - 2mx + m^2 - n^2 = 0.

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