Chapter 4.5, Problem 82S

To determine

To find: the value of ${\text{b}}^{\text{2}}\text{-4ac}$ for the given value of a, b and c.

Answer to Problem 82S

The value of ${\text{b}}^{\text{2}}\text{-4ac}$ is $73$ .

Explanation of Solution

Given:

  $\text{a=-2,b=-7,c=3}$ .

Concept used:

According to the general equation of quadratic equation:

  ${\text{ax}}^{\text{2}}\text{+bx+c=0}$ .

Discriminant is denoted by $\text{D}$ which is equal to ${\text{b}}^{\text{2}}\text{-4ac}$ which is used to find the solution of quadratic equation.

  $\text{x=}\frac{\text{-b±}\sqrt{\text{D}}}{\text{2a}}$ or $\text{x=}\frac{\text{-b±}\sqrt{{\text{b}}^{\text{2}}\text{-4ac}}}{\text{2a}}$ .

  ${\text{D=b}}^{\text{2}}\text{-4ac}$ .

Calculation:

According to the given:

  $\text{a=-2,b=-7,c=3}$ .

According to the general equation of quadratic equation:

  ${\text{ax}}^{\text{2}}\text{+bx+c=0}$ and $\text{a=-2,b=-7,c=3}$ .

  ${\text{b}}^{\text{2}}\text{-4ac}$ is also called the discriminant of the quadratic equation by putting the value $\text{a,b and c}$ :

  ${\text{b}}^{\text{2}}\text{-4ac=}{\left(\text{-7}\right)}^{\text{2}}\text{-4}\left(\text{-2}\right)\left(\text{3}\right)\text{=49+24=73}$ .

Hence, the value of ${\text{b}}^{\text{2}}\text{-4ac}$ is $73$ .