Question 1081768: The quadratic function has 2 real zeroes that differ by 18. Find the value of c.
f(x)= 2x^2 -24x+c
I've tried to plug in numbers but I dont get answers that differs by 18
Found 3 solutions by Boreal, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Quadratic formula is
x=(1/4)(-24+/- sqrt (576-8c))
The value +/- has to be 36, because divided by 4,it will be +/-9, and that will make the two roots 18 apart.
Therefore, sqrt (576-8c)=36
576-8c=1296
-8c=720
c=-90 ANSWER
roots are 15 and -3.
Answer by ikleyn(52817)  (Show Source):
You can put this solution on YOUR website! .
Let p and q are the roots.
Then, according to Vieta's theorem,
p + q =  = 12.
The second condition is
p - q = 18.
So, you have this system of equations
p + q = 12,
p - q = 18.
Add the equations. You will get
2p = 12 + 18 = 30.
Hence, p = 15.
Then q = 12 - p = 12 - 15 = -3.
Thus the roots are 15 and -3.
Then, according to Vieta's theorem,  = 15*(-3) = -45.
Then c = 2*(-45) = -90.
Answer. c = -90, and the roots are 15 and -3.
Answer by MathTherapy(10555)  (Show Source):
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