Use the discriminant to determine the number of real solutions of the equation. $$x ^ { 2 } - 5.79 x + 2.37 = 0$$
A) no real solutions
B) exactly one real solution
C) two real solutions
D) more than two real solutions
E) none of these

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2+bx+c=0$ is $\Delta=b^2-4ac$. If $\Delta>0$, the equation has two distinct real solutions. If $\Delta=0$, the equation has exactly one real solution. If $\Delta<0$, the equation has no real solutions. In this case, $a=1$, $b=-5.79$, and $c=2.37$. Therefore, $\Delta=(-5.79)^2-4(1)(2.37)=33.4881>0$. Thus, the equation has two real solutions. Therefore, the answer is C) two real solutions.

Use the Discriminant to Determine the Number of Real Solutions x2−5.79x+2.37=0x ^ { 2 } - 5.79 x + 2.37 = 0x2−5.79x+2.37=0

Use the Discriminant to Determine the Number of Real Solutions $x ^ { 2 } - 5.79 x + 2.37 = 0$