SOLUTION: In the equation 2x^2 — 3x + 4 = 0, what is the sum of the squares of the roots?

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Question 1132145: In the equation 2x^2 — 3x + 4 = 0, what is the sum of the squares of the roots?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Let "a" and "b" be the roots.


Then, according to Vieta's theorem


    a + b = 3%2F2,     (1)

    ab = 4%2F2 = 2.    (2)


Now,  a%5E2+%2B+b%5E2 = %28a%2Bb%29%5E2 - 2ab = %283%2F2%29%5E2 - 2*2 = 9%2F4-4 = -7%2F4.     ANSWER

Solved.


By the way, since the sum of squares is negative (as you see from the answer),
it means that the roots are COMPLEX NUMBERS.

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The lesson to learn from the solution is THIS : 

    You do not need to find the roots of the equation explicitly to answer the question.

So, my solution saved you from making tons of non-necessary calculations.