Determine the number of real solutions for each of the given equations. equation number of solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16

1 2 real

2. No real

3. 2 Real

4.  One real Multiplicity 2.

Step-by-step explanation:

Find the value of the discriminant D  (b^2 - 4ac) :-

1 . D = (1)^1 -4 * -3 * 12 = 1 + 144 = 145

D is positive so there re 2 real solutions.

2.  D = (-6)^2 - 4*2*5 = 36 - 40 = -4

D is negative so there are NO real solutions.

3.  D = (7)^2 - 4 * 1 * -11 = 49 + 44 = 93

2 real

solutions

4.  D = (-8)^2 - 4* -1 * -16 = 64 - 64

1 solution. Multiplicity 2.

1. 2 real

2. No real

3. 2 Real

4.  One real