Question 1132145
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<pre>
Let "a" and "b" be the roots.


Then, according to Vieta's theorem


    a + b = {{{3/2}}},     (1)

    ab = {{{4/2}}} = 2.    (2)


Now,  {{{a^2 + b^2}}} = {{{(a+b)^2}}} - 2ab = {{{(3/2)^2}}} - 2*2 = {{{9/4-4}}} = {{{-7/4}}}.     <U>ANSWER</U>
</pre>

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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<U>The lesson to learn from the solution is THIS</U> :


<pre>
    You do not need to find the roots of the equation explicitly to answer the question.
</pre>

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