real solutions

Question

Determine if each quadratic equation has real solutions. Choose Yes or No.
A. 12x^2-5=-3
B 2/3 x^2+7=11 (the x is not in the fraction, it is after)
C 2(x^2-3)=3(2x^2+1)
D 3x^2-1=8x^2+9
E 4(3x^2-7)=3(x^2-5)
Please show work for each letter. Thanks for the help. Have a great day! :)

Answer 1

You can look at the discriminant of each of these to determine whether the roots are real or not, TEW.

 

For any polynomial ax² + bx + c = 0 with real coefficients a, b, and c, the discriminant is

 

b² - 4ac

 

If b² - 4ac > 0, then there are real roots

 

If b² - 4ac < 0, then there are imaginary roots