Please help me! Due soon! The quadratic has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.

70/9

Step-by-step explanation:

We have the quadratic:

So, let’s find the roots of the quadratic. We will set the expression equal to 0:

Testing for factors, we can see that our quadratic isn’t factorable.

So, we can use the Quadratic Formula. The quadratic formula is given by:

In this case:

Therefore, by substitution:

Evaluate:

Simplify the square root:

Hence:

Reduce:

So, our roots are:

We want to find the sum of the squares of our two roots. So, let’s square each term:

Square. For the numerator, we can use the perfect square trinomial patten where:

Therefore:

Simplify:

Similarly, for the second root, we will have:

So:

Simplify:

Therefore, our sum will be:

Therefore, our final answer is 70/9.

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