Imaginary zeros of polynomials

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

  1. Discussing the Relationship Between the Discriminant and X-intercepts on a Graph
    Sketch and compare the following quadratic functions:
    y=2x2+x15y=2{x^2} + x - 15
    y=2x2+x+15y=2{x^2} + x + 15
    1. Locating the Regions of Imaginary Zeros on Polynomial Graphs
      Indicate the region on the graphs where the non-real zeros occur.
      i) f(x)=110(x+2)(x1)(x3)(x5)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(x)=110(x+2)(x1)(x28x+17)g\left( x \right) = \frac{1}{{10}}\left( {x + 2} \right)\left( {x - 1} \right)\left( {{x^2} - 8x + 17} \right)
      Topic Notes
      Based on the quadratic formula b±b24ac2a\frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} , non-real roots occur when the discriminant, b24ac{b^2} - 4ac , is negative. Non-real roots always occur in pairs.