Answer:
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 <em>squares</em> 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.