Chapter EP, Problem 5.2.7EP

To determine

To find: the solution of the given quadratic equation. If exact root can not be found find the two consecutive integers between which the roots are located.

Answer to Problem 5.2.7EP

Solution of the quadratic equation is $x=3,x=-\frac{1}{2}$.

Explanation of Solution

Given information:

The quadratic equation provided is

  $-5x+2x^2-3=0$

Concept used:

Solution of a quadratic equation can be found by factorizing the equation and equating each product with zero.

Calculation:

Consider the given equation.

  $-5x+2x^2-3=0$

Now, factorize the left hand side of the equation as shown:

  $\begin{array}{l}-5x+2x^2-3=0\\ 2x^2-5x-3=0\\ 2x^2-6x+x-3=0\\ \left(x-3\right)\left(2x+1\right)=0\end{array}$

Now, equate each factor with zero.

  $\begin{array}{c}x-3=0\\ x=3\end{array}$ or $\begin{array}{c}2x+1=0\\ x=-\frac{1}{2}\end{array}$

So, solution of the given quadratic equation is

  $x=3,x=-\frac{1}{2}$