Use the drop-down menus to complete the statements about the function p(x) = x(x - 1)+1.The value of a is .The value of b isThe value of cisThe value of the discriminant isThe quadratic function will intersect the x-axis times.

Accepted Solution

Answer: a=1, b=-1, c=1D=3i and quadratic function will not intersect x-axis.Step-by-step explanation:We have a quadratic function [tex]p(x) = x(x - 1)+1[/tex]or [tex]p(x) = x^{2}-x+1[/tex]This is of the form: [tex]p(x) = ax^{2}+bx+c[/tex]comparing the co-efficients of the two equations, a=1, b=-1, c=1Discriminant [tex]D=\sqrt{b^{2}-4ac }[/tex][tex]D=\sqrt{-3}[/tex] i.e D=3iwhere [tex]i=\sqrt{-1}[/tex]A quadratic function can have at-most of two roots. i.e, it can intersect x-axis, at 2 distinct points, or 1 identical point or not intersect at all.This can be seen from the value of it's discriminant.If D>0 ; Equation will have 2 distinct roots.If D=0 ; Both the roots of the equation are equal and 1 point of intersectionIf D<0 ; Roots are imaginary and function will not intersect x-axis.Here, D<0, and quadratic function will not intersect x-axis.