Chapter 9, Problem 1CA

To determine

To tell which discriminant of equations is positive, negative or zero

Answer to Problem 1CA

The answer is as follows.

Explanation of Solution

Given information:

  $\begin{array}{l}f(x)=0\\ g(x)=0\\ h(x)=0\\ j(x)=0\end{array}$

  

Calculation:

It is known,

If $D>0,$ 2 real solutions.

If $D=0,$ 1 real solution.

If $D<0,$ 2 imaginary solutions.

Number of intercepts are the number of solutions of a quadratic equation.

For $f(x)=0$ ,

There is no x -intercept, it means the solutions are imaginary. Hence, the determinant is negative.

For $h(x)=0$ ,

There is 1 x -intercept, it means there is 1 solution. Hence, the determinant is 0.

For $g(x)=0$ ,

There are 2 x -intercepts, it means the solutions are real. Hence, the determinant is positive.

For $j(x)=0$ ,

There is 1 x -intercept, it means there is 1 solution. Hence, the determinant is 0.