Math CentralQuandaries & Queries


Question from Pranav, a student:

If ax^2+bx-5=0 has no real roots. Then d sign of 1) a+b-5
2) (25a-5b-5)(4a+2b-5) will be what ??

Hi Pranav,

Let $f(x) = a x^2 + b x - 5$ and notice that $f(0) = -5.$ Think of the graph of $y = f(x).$ Since $f(x) = 0$ has no real roots the graph does not cross the X-axis. But at $x = 0$ the point on the graph is below the X-axis so the entire graph is below the X-axis.

What is $f(1)?$


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