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.