For equation 7, there are two real solutions.
For equation 8, there is one real solution and one complex solution.
For equation 9, there are two complex solutions.
For equation 10, there are two complex solutions.
Based on the provided information, we can determine the number and type of solutions for each quadratic equation using the discriminant formula, b² - 4ac.
7. y = x²+6x+8
The discriminant for this equation is 62 – 4(1)(8) = 36 - 32 = 4.
Since the discriminant is positive, the equation has two real solutions.
8. y = x²-6x+9
The discriminant for this equation is (-6)2-4(1)(9) = 36 - 36 0.
Since the discriminant is zero, the equation has one real solution (a repeated root) and one complex solution.
9. y = 8x210x +4
The discriminant for this equation is 102 - 4(8)(4) = 100 - 160 = -60.
Since the discriminant is negative, the equation has two complex solutions. 10. y = x²+1
The discriminant for this equation is (-1)2 - 4(0)(1) = 1 - 4 = -3.
Since the discriminant is negative, the equation has two complex solutions.
In summary:
For equation 7, there are two real solutions.
For equation 8, there is one real solution and one complex solution.
For equation 9, there are two complex solutions.
For equation 10, there are two complex solutions.