# Imaginary zeros of polynomials

### Imaginary zeros of polynomials

#### Lessons

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.
• 1.
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)
$y=2{x^2} + x + 15$

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