Answer: D) 0, one real solution
A quadratic function is given of the form:
We can find the roots of this equation using the quadratic formula:
Where is named the discriminant. This gives us information about the roots without computing them. So, arranging our equation we have:
<em>Since the discriminant equals zero, then we just have one real solution.</em>
<h2>12. Find discriminant.</h2>Answer: D) -220, no real solution
In this exercise, we have the following equation:
So we need to arrange this equation in the form:
Thus:
So the discriminant is:
<em>Since the discriminant is less than one, then there is no any real solution</em>
<h2>13. Value that completes the squares</h2>Answer: C) 144
What we need to find is the value of such that:
is a perfect square trinomial, that are given of the form:
and can be expressed in squared-binomial form as:
So we can write our quadratic equation as follows:
Finally, the value of that completes the square is 144 because:
Answer: C)
What we need to find is the value of such that:
So we can write our quadratic equation as follows:
Finally, the value of that completes the square is
because:
In this problem, we need to find the length and width of a rectangle. We are given the area of the rectangle, which is 45 square inches. We know that the formula of the area of a rectangle is:
From the statement we know that the length of the rectangle is is one inch less than twice the width, this can be written as:
So we can introduce this into the equation of the area, hence:
The only valid option is because is greater than zero. Recall that we can't have a negative value of the width. For the length we have:
Finally:
The distance in miles between mars and a satellite is given by the equation:
where is the number of hours it has fallen. So we need to find when the satellite will be 452 miles away from mars, that is,
:
Finally, <em>the satellite will be 452 miles away from mars in 6 hours.</em>