Final answer:
To find the discriminant of the quadratic equation 7x²+4x+5=-2, first put in standard form: 7x²+4x+7=0, then calculate the discriminant Δ=b²-4ac, which gives Δ=-180, indicating no real solutions.
Step-by-step explanation:
The student has been given the quadratic equation 7x²+4x+5=-2 and is asked to put it in standard form and to calculate the discriminant. To put it in standard form, we first need to move all terms to one side, yielding 7x²+4x+7=0.
Now, the standard form for a quadratic equation is ax²+bx+c=0. In this case, a=7, b=4, and c=7. The discriminant of a quadratic equation is given by the formula Δ=b²-4ac. Applying this to our equation, the discriminant is Δ=4²-(4· 7· 7), which simplifies to Δ=16-196, which further simplifies to Δ=-180.
A negative discriminant indicates that the quadratic equation has no real solutions.