SOLUTION: Could please explain to me how to solve: h=-16t^2+21t+40

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Could please explain to me how to solve: h=-16t^2+21t+40      Log On


   

Question 153470: Could please explain to me how to solve: h=-16t^2+21t+40
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
There are many ways to solve a quadratic polynomials For me, unless the problem requires a specific method OR unless the equation is simple enough to 'factor' in my head, I prefer to use the quadratic equation.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Just plug in -16 for a, 21 for b and 40 for c.
Another way to solve, if you have a graphing calculator, is to plot the graph and then see where the the plot crosses the x axis.
In either case, you get the same answers
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B21x%2B40+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2821%29%5E2-4%2A-16%2A40=3001.

Discriminant d=3001 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+3001+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2821%29%2Bsqrt%28+3001+%29%29%2F2%5C-16+=+-1.05566824060029
x%5B2%5D+=+%28-%2821%29-sqrt%28+3001+%29%29%2F2%5C-16+=+2.36816824060029

Quadratic expression -16x%5E2%2B21x%2B40 can be factored:
-16x%5E2%2B21x%2B40+=+-16%28x--1.05566824060029%29%2A%28x-2.36816824060029%29
Again, the answer is: -1.05566824060029, 2.36816824060029. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B21%2Ax%2B40+%29