Question

Use the drop-down menus to complete the statements about the function p(x) = x(x - 1)+1.

Answer 1

Answer: a=1, b=-1, c=1

D=3i and quadratic function will not intersect x-axis.

Step-by-step explanation:

We have a quadratic function $p(x) = x(x - 1)+1$

or $p(x) = x^{2}-x+1$

This is of the form:

$p(x) = ax^{2}+bx+c$

comparing the co-efficients of the two equations,

a=1, b=-1, c=1

Discriminant $D=\sqrt{b^{2}-4ac }$

$D=\sqrt{-3}$ i.e D=3i

where $i=\sqrt{-1}$

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 intersection

If D<0 ; Roots are imaginary and function will not intersect x-axis.

Here, D<0, and quadratic function will not intersect x-axis.

Answer 2

Answer:

The value of a is 1

The value of b is -1

The value of c is 1

The value of the discriminant is -3

The quadratic function will intersect the x-axis 0 times

Step-by-step explanation:

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