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

Answer 1

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 not intersects the  x-axis.

Explanation:

The standard form of a quadratic equation is,

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

The given function is,

$p(x)=x(x-1)+1$

It can be written as,

$p(x)=x^2-x+1$

By comparing this equation with the standard form of quadratic equation. we get,

$a=1$

$b=-1$

$c=1$

The formula for discriminant is,

$D=b^2-4ac$

$D=(-1)^2-4(1)(1)$

$D=1-4$

$D=-3$

The value of the discriminant is -3.

If D<0, it means the function have no real roots.

If D=0, it means function have one real roots.

If D>0, it means function have two real roots.

Since D<0 it means the function have no real roots. So the function will not intersect the x-axis at any point.

Answer 2

A is 1
b is -1
c is 1
discriminant is -3
x axis is 0