Question

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 is
The value of cis
The value of the discriminant is
The quadratic function will intersect the x-axis times.

Answer 1

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

Explanation:

I did the assignment

Answer 2

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

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

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=√(-3)` i.e D=3i

where
`i=√(-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.