Find all the real solutions for the equation:

Question

Solve the equation for all of the real solutions and show work :

2x²-3x+7

Answer 1

The real solutions would be where the graph of this equation (a parabola) crosses the x-axis. We can see because the 2 in front of the x² is positive that the parabola opens up and therefore means that the y-value of the vertex has to be negative. The x-value can be found by x=-b/2a where b=-3 and a=2: x=-(-3)/2(2)--->x= 3/4. Putting this value in for x we find that y=2(3/4)² -3(3/4)+7--->y=2(9/16)-(9/4)+7--->(9/8)-(9/4)+7--->47/8 which is positive, so there is no real solutions to this.

Hope this helps!

Answer 2

Let's look at the discriminant to see how many real solutions there are. The discriminant is given as:

b² - 4ac

where a = 2, b = -3 and c = 7. Plug those numbers into the discriminant formula above. If the discriminant is positive (> 0), then there are two real solutions. If the discriminant equals 0, there is one real solution. If the discriminant is less than zero, there are no real solutions.