How do you know there is no real solution to the quadratic equation x2+x+14=0?
because the discriminant (b^2-4ac) is negative.
The easiest way to justify this is to visualize the graph. We know from the first the signs of this equation that this quadratic opens upwards and know that it is shifted to be above the x-axis, so the quadratic never crosses the x-axis and therefore has no roots.
You could justify this by finding the discriminant, sqrt(b^2 - 4ac). Since this answer would yield a negative number, both roots lie in the complex plane.
To determine if there is a real solution to the quadratic equation x^2 + x + 14 = 0, we can use the discriminant. The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the expression b^2 - 4ac.
In this case, a = 1, b = 1, and c = 14. Substituting these values into the discriminant formula, we have:
Discriminant = (1)^2 - 4(1)(14)
= 1 - 56
= -55
The discriminant is negative (-55), which indicates that there are no real solutions to the quadratic equation.
When the discriminant is negative, it means that the quadratic equation does not intersect the x-axis, and therefore, no real solutions exist.