Use a graphing calculator to determine the number of real solutions of the quadratic equation $4 x ^ { 2 } - 3 x + 9 = 0$ .
A)one real solution
B)no real solutions
C)two real solutions

Question

Quizplus · Accepted Answer

Using the quadratic formula, we get 
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
where $a=4$, $b=-3$, and $c=9$. Evaluating under the radical, we get
$$b^2-4ac=(-3)^2-4(4)(9)=-111<0$$
Since the discriminant is negative, there are no real solutions to the equation.

Use a Graphing Calculator to Determine the Number of Real 4x2−3x+9=04 x ^ { 2 } - 3 x + 9 = 04x2−3x+9=0

Use a Graphing Calculator to Determine the Number of Real $4 x ^ { 2 } - 3 x + 9 = 0$