Zeros of a Quadratic Math Example 4

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Example 4

hard
How many zeros does f(x)=x2+4f(x) = x^2 + 4 have over the reals?

Solution

  1. 1
    x2+4=0⇒x2=−4x^2 + 4 = 0 \Rightarrow x^2 = -4. No real number squared gives −4-4.
  2. 2
    Discriminant: 0−16=−16<00 - 16 = -16 < 0. Zero real zeros.

Answer

Zero real zeros.
When the discriminant is negative, the parabola lies entirely above (or below) the xx-axis and has no real zeros.

About Zeros of a Quadratic

The zeros (or roots) of a quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + c are the values of xx where f(x)=0f(x) = 0. Graphically, they are the xx-intercepts of the parabola.

Learn more about Zeros of a Quadratic →

More Zeros of a Quadratic Examples

Example 1 easy

Find the zeros of [formula].

Example 2 medium

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Example 3 easy

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