How do you find the discriminant and how many solutions does 11x2−9x−1=0? have?

1 Answer
Jim H
May 1, 2015

The discriminant is the thing you take the square root of in the

quadratic formula:

ax2+bx+c=0 has solution(s): x=−b±√b2−4ac2a

The discriminant is b2−4ac

If a,b and c are real numbers, then:
If the discriminant is positive, then there are two real solutions.
ssss One when we add and another when we subtract.

If the discriminant is 0, then there is one real solutions.
ssss Since √0=0, adding and subtracting do not give us different answers.

If the discriminant is positive, then there are two imaginary solutions.
ssss Since the square root of a negative is imaginary, we get imaginary solutions.

In 11x2−9x−1=0, we have

a=11, b=−9 and c=−1, so the discriminant is:

b2−4ac=(−9)2−4(11)(−1), which is equal to :

81+44=125

The equation has two real solutions.
ssss One when we add √125 and another when we subtract √125.

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