SOLUTION: Find the quadratic equation with integral coefficient whose roots are negative 2 and three fifths.

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Question 227466: Find the quadratic equation with integral coefficient whose roots are negative 2 and three fifths.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
An equation of the form:
a%28x-r%5B1%5D%29%28x-r%5B2%5D%29... = 0 will give you an equation whose roots are r%5B1%5D, r%5B2%5D, .... where "a" is an optional constant.

So the equation you want. with roots of -2 and 3%2F5, would be:
%28x+-+%28-2%29%29%28x+-+3%2F5%29+=+0
Simplifying this we get:
%28x+%2B+2%29%28x+-+3%2F5%29+=+0
x%5E2+-+%283%2F5%29x+%2B+2x+-+6%2F5+=+0
Since we want integral coefficients we'll do that now (so we can avoid adding with fractions). To eliminate the fractions, multiply both sides by the Lowest Common Denominator (LCD), which is 5 in this equation:
5%28x%5E2+-+%283%2F5%29x+%2B+2x+-+6%2F5%29+=+5%280%29
5x%5E2+-3x+%2B+10x+-6+=+0
5x%5E2+%2B7x+-6=0
which is the desired equation.