SOLUTION: solve the following by factoring: 5t squared - 10t = 0 x squared - 3x - 10 = 0 if f(x) = 3x squared + 5x -2 find f(-2) f(4) solve 3x squared + 19x - 14 = 0 u

Algebra ->  Rational-functions -> SOLUTION: solve the following by factoring: 5t squared - 10t = 0 x squared - 3x - 10 = 0 if f(x) = 3x squared + 5x -2 find f(-2) f(4) solve 3x squared + 19x - 14 = 0 u      Log On


   

Question 137421: solve the following by factoring:
5t squared - 10t = 0
x squared - 3x - 10 = 0
if f(x) = 3x squared + 5x -2 find
f(-2)
f(4)
solve
3x squared + 19x - 14 = 0 using quadratic formula.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by factoring:
1)
5t%5E2-10t+=+0 Factor out 5t from each term:
5t%28t-2%29+=+0 Now apply the zero products rule;
5t+=+0 and/or t-2+=+0
If 5t+=+0 then t+=+0
If t-2+=+0 then t+=+2
2)
x%5E2-3x-10+=+0 Factor the trinomial.
%28x%2B2%29%28x-5%29+=+0 Apply the zero products rule.
x%2B2+=+0 and/or x-5+=+0
If x%2B2+=+0 then x+=+-2
If x-5+=+0 then x+=+5
3)
f%28x%29+=+3x%5E2%2B5x-2 find: f(-2). Just substitute -2 everywhere there is an x in the function.
f%28-2%29+=+3%28-2%29%5E2%2B5%28-2%29-2 Simplify.
f%28-2%29+=+3%284%29%2B%28-10%29-2
f%28-2%29+=+12-10-2
f%28-2%29+=+0
Find: f(4)
f%284%29+=+3%284%29%5E2%2B5%284%29-2
f%284%29+=+3%2816%29%2B20-2
f%284%29+=+48%2B20-2
f%284%29+=+66
4) Solve for x using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
3x%5E2%2B19x-14+=+0 Here, a = 3, b = 19, and c = -14. Making the appropriate substitutions, we get:
x+=+%28-19%2B-sqrt%28%2819%29%5E2-4%283%29%28-14%29%29%29%2F2%283%29 Simplify this:
x+=+%28-19%2B-sqrt%28361-%28-168%29%29%29%2F6
x+=+%28-19%2B-sqrt%28529%29%29%2F6
x+=+%28-19%2B23%29%2F6 or x+=+%28-19-23%29%2F6
x+=+2%2F3 or x+=+-7