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 answer fasrt

No. of real solns depends on the term b^2 - 4ac for y = ax^2 + bx + c
if its <0, no real soln
its =0, 1 real soln
its >0, 2 real solns

for
 y = -3x2 + x + 12, 1^2-4(-3)(12) > 0, two solns
 y = 2x2 - 6x + 5, -6^2-4(2)(5)  < 0, no soln
 y = x2 + 7x - 11, 7^2-4(1)(-11) > 0, two solns
 y = -x2 - 8x - 16, -8^2-4(-1)(-16) = 0, one soln