How you can tell that the quadratic function y=x^2 +6x+15 has no real zeroes without graphing the function?

1 Answer
Douglas K.
Nov 16, 2016

When given a quadratic equation in standard form:

y = ax^2 + bx + c or x = ay^2 + by + c

Check the value of the determinant:

b^2 - 4(a)(c)

If it is greater than zero, the equation will have two real roots.
If it is equal to zero, the equation will have one root (a.k.a. a repeated root).
If it is less than zero, the equation will have complex conjugate pair of roots.

In the case of the given equation

b^2 - 4(a)(c) = 6^2 - 4(1)(15) = -24

This equation will have a complex conjugate pair of roots (-3 + sqrt6i) and (-3 - sqrt6i) .

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