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How do I get from x^2 + ax+16 =0 to a^2−4(1)(16)=0?
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laurens876
How do I get from x^2 + ax+16 =0 to a^2−4(1)(16)=0?

If the quadratic equation is \(ax^2 + bx + c = 0\), then the values of x are:

\(x = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

and

\(x = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

where \(b^2 - 4ac\) is the discriminant

If \(b^2 - 4ac > 0\), x has two distinct values

If \(b^2 - 4ac = 0\), x has one value

If \(b^2 - 4ac < 0\), x has no real value

In the question we have, comparing \(x^2 + ax + 16 = 0\) with \(ax^2 + bx + c = 0\), we get a = 1, b = a, and c = 16.

Substituting in \(b^2 - 4ac\) => \(a^2 - 4(1)(16)\)

We are told that x has one value, therefore \(a^2 - 4(1)(16) = 0\)
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