Chapter 9, Problem 54SGR

To determine

To compute the discriminant of the equation and determine the number of real solutions.

Answer to Problem 54SGR

The discriminant is 76 . Since it is positive, there are 2 real solutions.

Explanation of Solution

Given information :

The equation is $-6x^2+2x+3=0$ .

Formula used :

Discriminant is found out using the formula $b^2-4ac$ , where ‘a’, ‘b’ and ‘c’ are the coefficients of the equation.

The solutions can be determined by:

If discriminant is negative, then there are no real solutions.

If discriminant is zero, then there is 1 real solution.

If discriminant is positive, then there are 2 real solutions.

Calculation :

  $-6x^2+2x+3=0$

Given equation.

Hence, $a=-6$ , $b=2$ and $c=3$ .

  ${\left(2\right)}^2-4\times \left(-6\right)\times 3$

Putting the values in the formula.

  $=4+72$

Simplifying

  $=76$

This is the discriminant. Since it is positive, there are 2 real solutions.