Math CentralQuandaries & Queries


Question from Alberto, a student:

The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:

(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0

Explain the choice.

We have two responses for you


Think about trying to plot the graph of f(x) = ax2 + bx + c. What can you say about the point (1, f(1))? Is it above the x-axis or below the x-axis? What about (0, f(0))? Since ax2 + bx + c has no real roots the graph of f(x) = ax2 + bx + c never crosses the x-axis.



Two hints:

-what do you know about b^2 - 4ac from the first statement?

-consider the second statement separately for b>0 and b<0. Does one of these yield a contradiction with a little work?

Good Hunting!


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