Chapter 9.5, Problem 38PPS

To determine

The value of the discriminant of the equation $0.5x^2-2x=-2$ and find the number of real solutions.

Answer to Problem 38PPS

  $D=0,\text{ there are two same real roots}$

Explanation of Solution

Given information:

The given equation, $0.5x^2-2x=-2$

Concept used:

• The discriminant is given by, $D=b^2-4ac$
• For a quadratic equation $a{x}^2+bx+c=0$ the number of roots depend on:
• If discriminant is negative, $b^2-4ac<0$, then there is no real roots
• If discriminant is zero, $b^2-4ac=0$, then there are two same real roots
• If discriminant is positive, $b^2-4ac>0$, then there are two distinct real roots

Calculation:

To find the discriminant of the given quadratic equation first rewrite the given equation in standard form by add both sides by 2 So it gives

  $0.5x^2-2x+2=0$

Now compare this equation with the general equation, $a{x}^2+bx+c=0$ to get the value of the variables, $a=0.5,b=-2,c=2$ . So, the discriminant of the given equation is

  $\begin{array}{c}D=b^2-4ac\\ ={\left(-2\right)}^2-4\left(0.5\right)\left(2\right)\\ =4-4\\ =0\end{array}$

So, the discriminant of the given equation is $0$ .

Since the discriminant is, so there are there are two same real roots of the given equation.