Answer
no real solution
Work Step by Step
RECALL
The nature of solutions using the quadratic equation $ax^2+bx+c=0$ can be determined using the value of its discriminant $b^2-4ac$.
If the value of the discriminant is:
(1) negative, then the equation has no real solutions;
(2) zero, then the equation has one repeated solution; and
(3) positive, then there are two unequal solutions.
The given quadratic equation has :
$a=1
\\b=4
\\c=7$
Solve for the discriminant to obtain:
$=b^2-4ac
\\=4^2-4(1)(7)
\\=16-28
\\=-12$
The discriminant is negative, so the equation has no real solutions.
