Multiple choice

The roots of the quadratic equation x2 - 10x + 22 = 0 are m and n. Find the value of (m2 + n2)(m + n).

  1. 250

  2. 340

  3. 560

  4. 600
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C Correct answer
Explanation

For x^2 - 10x + 22 = 0, m+n = 10 and mn = 22. m^2 + n^2 = (m+n)^2 - 2mn = 100 - 44 = 56. The value of (m^2 + n^2)(m + n) = 56 * 10 = 560.

AI explanation

For a quadratic equation ax^2 + bx + c = 0, the sum of roots (m + n) is -b/a and the product of roots (mn) is c/a. Here, (m + n) is 10 and mn is 22. Using the algebraic identity m^2 + n^2 = (m + n)^2 - 2mn, we find m^2 + n^2 = 10^2 - 2(22) = 100 - 44 = 56. Multiplying this sum of squares by the sum of the roots gives the required value, which is 56 * 10 = 560.

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