As easy as One Two Three

Algebra Level 3

Given the quadratic equation $ax^2+bx+c=0$ and $x^2+2x+3=0$ have a common root with $a, b, c>0$ .

If $a,b,c$ are sides of a triangle, classify what type of triangle this triangle is.

Not possible Isosceles Scalene Equilateral

1 solution

Alex Li
May 7, 2015

The roots of the polynomial $x^2+2x+3=0$ are complex, because the discriminant is negative. However, complex roots always come in conjugate pairs, so the polynomial must have the same roots. This occurs when $a:b:c=1:2:3$ , which violates the triangle inequality, so no triangle exists.

As easy as One Two Three

1 solution

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