This document provides the solution to a math question about solving a quadratic equation ax^2 + bx + c = 0, where a+b+c < 0 and c < 0. It states that because a+b+c < 0 and c < 0, the equation must have roots between 0 and 1, as f(1)f(0) = (a+b+c)c < 0. Therefore, the solutions to the quadratic equation are between 0 and 1.

1. Today’s Math Question 2009 11 8
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ax2 + bx + c = 0 a+b+c < 0 c<0

2. Today’s Math Answer
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f (x) = ax2 + bx + c
x
f (1) = a + b + c, f (0) = c
a+b+c<0 , c 0
f (1)f (0) < 0
f (x) = 0 0 x<1
a+b+c<0 f (0) = c < 0 ......