Question

Select all the correct locations on the image. Identify which functions have complex roots by selecting the function names on the provided coordinate plane.

Answer 1

The parabolae b, d and f seen in the real coordinate plane have complex roots.

What is the graphical criterion to determine what second order polynomial has complex roots?

Second order polynomials are algebraic equations of the form:

$y = a\cdot x^{2}+b\cdot x + c$   (1)

Where:

• a, b, c - Coefficients
• x - Independent variable
• y - Dependent variable

A value of x is a root of the polynomial for y = 0, which can real or complex but not both according to the discriminant of the quadratic formula. If the polynomial has no real roots, then it does not pass through the x-axis in the real coordinate plane.

Therefore, the parabolae b, d and f seen in the real coordinate plane have complex roots. $\blacksquare$

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