Use the discriminant to determine the number of real solutions of $x ^ { 2 } - 2 x + 7 = 0$ .
A)two real solutions
B)one real solution
C)no real solutions

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2+bx+c=0$ is given by $b^2-4ac$. If the discriminant is negative, then there are no real solutions; if the discriminant is zero, then there is one real solution; and if the discriminant is positive, then there are two real solutions. 
For the given equation, we have $a=1$, $b=-2$, and $c=7$. So the discriminant is:
\begin{align*}
b^2-4ac &= (-2)^2-4(1)(7) \
&= 4-28 \
&= -24
\end{align*}
Since the discriminant is negative, there are no real solutions for the given equation. Therefore, the best choice is C, no real solutions.

Use the Discriminant to Determine the Number of Real Solutions x2−2x+7=0x ^ { 2 } - 2 x + 7 = 0x2−2x+7=0

Use the Discriminant to Determine the Number of Real Solutions $x ^ { 2 } - 2 x + 7 = 0$