Question 697057
{{{ax^2+bx+c=0}}}


a)


with roots of {{{6}}} and {{{7}}}

{{{(x-x1)(x-x2)=0}}}...where {{{x1}}} and {{{x2}}} are given roots


{{{(x-6)(x-7)=0}}}


{{{x^2-7x-6x+42=0}}}



{{{x^2-13x+42=0}}}.......a quadratic equation


{{{ graph( 600,600, -5, 20, -5, 130, x^2-13x+42) }}} 


b) What would happen to the roots if you {{{multiplied}}} both sides of the
equation in part a) by {{{3}}}

{{{(x^2-13x+42)*3=0*3}}}

{{{3x^2-39x+126=0}}}


{{{ graph( 600,600, -5, 20, -5, 130, 3x^2-39x+126) }}} 


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( 600,600, -5, 20, -5, 130, 3x^2-39x+126,x^2-13x+42) }}}