Multiple choice

Sum of the squares of the roots of the quadratic equation $\displaystyle { x }^{ 2 }-5x+2=0$ is :

  1. 15

  2. 17

  3. 33

  4. 21
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D Correct answer
Explanation

For x^2 - 5x + 2 = 0, sum of roots (a+b) = 5, product (ab) = 2. Sum of squares = a^2 + b^2 = (a+b)^2 - 2ab = 5^2 - 2(2) = 25 - 4 = 21.

AI explanation

For the quadratic equation x^2 - 5x + 2 = 0, the sum of the roots is 5 and the product is 2. The identity for the sum of squares is alpha^2 + beta^2 = (alpha + beta)^2 - 2(alpha)(beta). Substituting the known values gives 5^2 - 2(2), which is 25 - 4. The sum of the squares of the roots is 21.

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