Thread: Find the Positive Root Of The Following Equation

Positive root of the following equation:
34*x^2 + 68*x - 510
Recall:
a*x^2 + b*x + c
x1 = ( - b + sqrt ( b*b - 4*a*c ) ) / ( 2*a)


I have no idea how to go about doing this. Can someone help me out?

Divide both sides of the equation by 34.




By the quadratic formula,



The positive root is .


Alternatively, may be factored: . The roots are -5 and 3.

Originally Posted by gregzaj1

Positive root of the following equation:
34*x^2 + 68*x - 510

First, you understand that this is NOT an equation, don't you? I think you meant which is an equation because it has "=" but I had to guess at the "0"

Recall:
a*x^2 + b*x + c

Again, that is NOT an equation. You mean .
Now, compare that with your . You should see that a= 34, b= 68, and c= -510

x1 = ( - b + sqrt ( b*b - 4*a*c ) ) / ( 2*a)

So "b*b- 4*a*c" is (68)(68)- 4(34)(-510)= 4624+ 69360= 73984 and the square root is 272.
-b+sqrt(b*b- 4*a*c)= -68+ 272= 204. 2*a= 2*34= 68 so x= 204/68= 3.

That wasn't so hard was it?

(If you are very clever, like richard1234, you might recognise that 68= 2(34) and 510= 15(34) so dividing through by 34 at the start simplifies the numbers.)

I have no idea how to go about doing this. Can someone help me out?