Points A, B, and C are plotted in that order and are all collinear. If AB = x^2, BC=x^2+5 and Ac = 3x^2+7x+17, find AC.

Question

Word Problems involving quadratic equations

Answer 1

Collinear means that these points form a line segment...or that B is on segment AC. So AB + BC = AC.

 

So x²+x²+ 5 = 3x²+7x+17

 

0 = x² + 7x + 12

0 = (x+3)(x+4)

 

so x=-3 or x=-4.

 

If x=-3, your segment become 9, 14 and 23.

 

If x=-4, your segment becomes 16, 21 and 37.

 

So you have 2 possible answers.

 

Hope this helped.