Based on the quadratic formula $\frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$ , non-real roots occur when the discriminant,
${b^2} - 4ac$ , is negative. Non-real roots always occur in pairs.

# Imaginary zeros of polynomials

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Examples

**Discussing the Relationship Between the Discriminant and X-intercepts on a Graph**

Sketch and compare the following quadratic functions:

i) $y=2{x^2} + x - 15$

ii) $y=x^2+4x+4$

iii) $y=2{x^2} + x + 15$**Locating the Regions of Imaginary Zeros on Polynomial Graphs**

Indicate the region on the graphs where the non-real zeros occur.

i) $f\left( x \right) = \frac{1}{{10}}\left( {x + 2} \right)\left( {x - 1} \right)\left( {x - 3} \right)\left( {x - 5} \right)$

ii) $g\left( x \right) = \frac{1}{{10}}\left( {x + 2} \right)\left( {x - 1} \right)\left( {{x^2} - 8x + 17} \right)$