SOLUTION: 10. a) Write a quadratic equation in the form ax 2  bx  c  0 with roots of 6 and 7. b) What would happen to the roots if you multiplied both sides of the equation in

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 10. a) Write a quadratic equation in the form ax 2  bx  c  0 with roots of 6 and 7. b) What would happen to the roots if you multiplied both sides of the equation in       Log On


   

Question 697057: 10. a) Write a quadratic equation in the
form ax
2
 bx  c  0 with roots
of 6 and 7.
b) What would happen to the roots if
you multiplied both sides of the
equation in part a) by 3? Explain.
Found 2 solutions by lwsshak3, MathLover1:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The roots would be the same but the shape of the curve (parabola) would be narrower or steeper, in effect increasing the slope of the curve.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
ax%5E2%2Bbx%2Bc=0

a)

with roots of 6 and 7
%28x-x1%29%28x-x2%29=0...where x1 and x2 are given roots

%28x-6%29%28x-7%29=0

x%5E2-7x-6x%2B42=0


x%5E2-13x%2B42=0.......a quadratic equation

+graph%28+600%2C600%2C+-5%2C+20%2C+-5%2C+130%2C+x%5E2-13x%2B42%29+

b) What would happen to the roots if you multiplied both sides of the
equation in part a) by 3
%28x%5E2-13x%2B42%29%2A3=0%2A3
3x%5E2-39x%2B126=0

+graph%28+600%2C600%2C+-5%2C+20%2C+-5%2C+130%2C+3x%5E2-39x%2B126%29+

the roots will remain same, if you multiply or divide both sides of an equation by the same number, it does not change the equality of the equation

however, the absolute value of the "a" value increases from 1 to 3, and the graph becomes "steeper"
here are both parabolas on a graph:
+graph%28+600%2C600%2C+-5%2C+20%2C+-5%2C+130%2C+3x%5E2-39x%2B126%2Cx%5E2-13x%2B42%29+