SOLUTION: An original quadratic equation for x is of the form: x^2+bx+c=0. If c is increased by 4, the roots for x of the resulting equation are equal, but if the original c is decrease

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: An original quadratic equation for x is of the form: x^2+bx+c=0. If c is increased by 4, the roots for x of the resulting equation are equal, but if the original c is decrease      Log On


   

Question 179376: An original quadratic equation for x is of the form: x^2+bx+c=0. If c is increased by 4, the roots for x of the resulting equation are equal, but if the original c is decreased by 5 one of the roots for x in this resulting equation is twice the other. Find the product of the roots for x in the original quadratic equation.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the roots are r%5B1%5D and r%5B2%5D, I can write
%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0
x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5D%2Ar%5B2%5D+=+0
the original equation is of the form
x%5E2+%2B+bx+%2B+c+=+0
c+=+r%5B1%5D%2Ar%5B2%5D
(1) c+%2B+4+=+%28r%5B1%5D%29%5E2
c+-+5+=+r%5B1%5D%2A%28r%5B1%5D%2F2%29
(2) 2%2A%28c+-+5%29+=+%28r%5B1%5D%29%5E2
Subtract (1) from (2)
2c+-+10+-+c+-+4+=+0
c+=+14
The product of the roots is 14
check:
(1) c+%2B+4+=+%28r%5B1%5D%29%5E2
18+=+%28r%5B1%5D%29%5E2
r%5B1%5D+=+sqrt%2818%29
r%5B1%5D+=+3%2Asqrt%282%29
c+=+r%5B1%5D%2Ar%5B2%5D
14+=+3%2Asqrt%282%29%2A+r%5B2%5D
r%5B2%5D+=+%2814%2Asqrt%282%29%29%2F6
r%5B1%5D%2Ar%5B2%5D+=+%283%2Asqrt%282%29%29%2A%2814%2Asqrt%282%29%29%2F6
r%5B1%5D%2Ar%5B2%5D+=+%2814%2A2%29%2F2
14+=+14
OK