Whats the discriminant of this problem?

Question

x^2+3x-4=0

Find the discriminant, and determine the number of real solutions. Then solve

Answer 1

DISCRIMINANT:
Given the quadratic equation ax² + bx + c = 0, the value of the discriminant is b² - 4ac.

Here is how it works:
If b² - 4ac > 0, then there are 2 real solutions
If b² - 4ac = 0, then there is only 1 real solution
If b² - 4ac < 0, then there are no real solutions

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The equation is
x² + 3x - 4 = 0

The form of quadratic equation is
ax² + bx + c = 0

therefore,
a = 1, b = 3 and c = -4

We substitute it to the discriminant formula:
b² - 4ac = 3² - 4(1)(-4)

We simplify
b² - 4ac = 9 + 16

Therefore, the value of the discriminant is:
b² - 4ac = 25

Since 25 > 0, then the equation has 2 real solutions.

^_^

Answer 2

The discriminant of ax^2 + bx + c = 0 is b^2 - 4ac, so in this case it is 3^2 - 4(1)(-4), i.e. 9 + 16 = 25. It is positive, so there are two solutions.

The solutions are given by the formula
(-b +/- sqrt(b^2 - 4ac)) / (2a), i.e.
(-3 +/- 5) / 2
or 1, -4. However, in this case it's quicker just to factorise and solve:

0 = x^2 + 3x - 4 = (x + 4)(x - 1)
so the solutions are 1 and -4.