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

Question 1132145: In the equation 2x^2 � 3x + 4 = 0, what is the sum of the squares of the roots?
Answer by ikleyn(52777) (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 = ,     (1)

    ab =  = 2.    (2)


Now,   =  - 2ab =  - 2*2 =  = .     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.

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