Find the type of graph of a function with the same zero(s) as the provided functions: a) x2 + 5x + 8, b) x3 - 6x2 + 11x - 6
Quadratic functions are those functions that have almost two zeroes and the highest order is two. They are used in various fields of engineering and science to find values of different parameters. Cubic functions are those which have almost three zeroes. They are also used in many engineering applications.
Answer: For the equation x2 + 5x + 8, the graph is parabola which doesn't touch the x-axis, and for the equation x3 - 6x2 + 11x - 6, the graph cuts the x axis at 3 points.
Let's understand the solution.
a) For the equation x2 + 5x + 8:
⇒ Discriminant D = 52 - 4 × 8 = -7 < 0
b) For the equation x3 - 6x2 + 11x - 6:
After we simplify the equation, we get:
⇒ x3 - 6x2 + 11x - 6 = (x - 1) (x - 2) (x - 3)
Hence, the equation has three real roots, hence it cuts the x-axis three times.