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.

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m