MATH SOLVE

5 months ago

Q:
# 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 - 16pppppppllllllleeeeaaaassssseeeee ANSWER FASRT

Accepted Solution

A:

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

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