SOLUTION: Determine the quadratic equation if the difference of the squares of the roots is 95 and their difference is 5.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine the quadratic equation if the difference of the squares of the roots is 95 and their difference is 5.       Log On


   

Question 921337: Determine the quadratic equation if the difference of the squares of the roots is 95 and their difference is 5.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the roots be:
x%5B1%5D+and x%5B2%5D
the difference of the squares of the roots is 95
%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95.............eq.1
their difference is 5+

x%5B1%5D+-+x%5B2%5D=5 ............eq.2

solve the system:
%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95.............eq.1
x%5B1%5D+-+x%5B2%5D=5 ............eq.2
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start with x%5B1%5D-x%5B2%5D=5 ............eq.2 ...solve for+x%5B1%5D+
x%5B1%5D+=5%2Bx%5B2%5D+.............substitute in eq.1
%285%2Bx%5B2%5D+%29%5E2+-%28+x%5B2%5D%29%5E2=95.............eq.1....solve for+x%5B2%5D+
25%2B10x%5B2%5D+%2Bx%5B2%5D+%5E2+-%28+x%5B2%5D%29%5E2=95
25%2B10x%5B2%5D+%2Bcross%28x%5B2%5D+%5E2%29+-cross%28%28+x%5B2%5D%29%5E2%29=95
10x%5B2%5D+=95-25

10x%5B2%5D+=70
x%5B2%5D+=70%2F10
highlight%28x%5B2%5D+=7%29
go to+x%5B1%5D+=5%2Bx%5B2%5D+ plug in x%5B2%5D+=7
x%5B1%5D+=5%2B7
highlight%28x%5B1%5D+=12%29
roots are: 7 and 12
use zero product rule
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29 ...........plug in+x%5B1%5D+=12 and x%5B2%5D+=7
f%28x%29=%28x-12%29%28x-7%29
f%28x%29=x%5E2-7x-12x%2B7%2A12

highlight%28f%28x%29=x%5E2-19x%2B84%29

graph:

+graph%28+600%2C+600%2C+-15%2C+25%2C+-10%2C+100%2C+x%5E2-19x%2B84%29+