Question 1186822
Write the quadratic equation whose roots are −3 and − 4, and whose leading coefficient is 4. (Use the letter x to represent the variable.)
<pre>
If the leading coefficient were 1 and not 4, the quadratic equation would be:

{{{x^2}}}{{{""-""}}}{{{(matrix(3,1,SUM,OF,ROOTS))x}}}{{{""+""}}}{{{(matrix(3,1,PRODUCT,OF,ROOTS))}}}{{{""=""}}}{{{0}}} 

So we begin by finding that:

SUM OF ROOTS = (-3) + (-4) = -7

PRODUCT OF ROOTS (-3)(-4) = 12

So with leading coefficient 1, the answer would be 

{{{x^2}}}{{{""-""}}}{{{(-7)x}}}{{{""+""}}}{{{(12)}}}{{{""=""}}}{{{0}}}

simplify

{{{x^2}}}{{{""+""}}}{{{7x}}}{{{""+""}}}{{{12}}}{{{""=""}}}{{{0}}} 

To make it have leading coefficient of 4, simply multiply through by 4:

{{{4x^2}}}{{{""+""}}}{{{28x}}}{{{""+""}}}{{{48}}}{{{""=""}}}{{{0}}}

Edwin</pre>