Question

What is the number of real solutions?
-11x^2=x+11
a. cannot be determined
b. one solution
c. two solutions
d. no real solutions

Answer 1

First write that quadratic equation as -11x^2 - x - 11 = 0.
Next, compute the discriminant, b^2 - 4ac. The discriminant tells about the nature of the roots of a quadratic equation.

So a = -11, b = -1, c = -11.

So, b^2 - 4ac = (-1)^2 - 4(-11)(-11) = 1 -484 = -483.

Since the discriminant is less than 0, the roots are imaginary (complex) numbers.

Answer 2

Note:

1) Before computing the discriminant, make sure you set the quadratic equal to zero! Just like what I did above.

2) If the discriminant is graeter than or equal to zero, the roots are real numbers.

3) If the discriminant is exactly zero, then there is only one real root (solution) of the equation.

Answer 3

4) If the discriminant is greater than zero AND a perfect square, like 25, then the two roots are real and rational numbers.

5) If the discriminant is greater than zero AND a non-perfect square, like 13, then the two roots are real and irrational numbers.

So now, I gave you everything you need to know about the discriminant.

Answer 4

@Easyaspi314 so the answer would be no real solution because the number is negative

Answer 5

yes, becuase the discriminant < 0.