Question

Please help me solve this problem, and someone please clearly explain to me how to solve it.

1.) Use the value of the discriminant to determine if the given trinomials has 2 real solutions, 1 real solution, or no real solutions.
a. x2 − 4x − 7 = 0
b. 4r2 + 11r − 3 = 0
c. 3m2 + 7 = 0
d. t2 + 2t + 1 = 0​

Answer 1

Explanation:

For a trinomial ax² + bx + c = 0, the discriminant is b² − 4ac.

If the discriminant is positive, there are 2 real solutions.

If the discriminant is 0, there is 1 real solution.

If the discriminant is negative, there are no real solutions.

a) x² − 4x − 7 = 0

Here, a = 1, b = -4, and c = -7.

b² − 4ac = (-4)² − 4(1)(-7) = 44

The discriminant is positive, so there are 2 real solutions.

b) 4r² + 11r − 3 = 0

Here, a = 4, b = 11, and c = -3.

b² − 4ac = (4)² − 4(11)(-3) = 148

The discriminant is positive, so there are 2 real solutions.

c) 3m² + 7 = 0

Here, a = 3, b = 0, and c = 7.

b² − 4ac = (0)² − 4(3)(7) = -84

The discriminant is negative, so there are no real solutions.

d) t² + 2t + 1 = 0

Here, a = 1, b = 2, and c = 1.

b² − 4ac = (2)² − 4(1)(1) = 0

The discriminant is zero, so there is 1 real solution.