# example of a quadratic without real solutionsGive example of a quadratic without real solutions

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A quadratic equation of the form ax^2 + bx + c = 0, does not have real solutions if b^2 - 4ac < 0 or b^2 < 4ac

Using the given relation we can find an unlimited number of examples. A few of which are

4x^2 - x + 1 = 0

x^2 - x + 1 = 0

2x^2 - x + 1 = 0

x^2 + x + 1 = 0

We'll take as example the quadratic equation: 2x^2 + 6x + 5 = 0

2x^2 + 6x + 5 = 0

Now, we'll verify if the equation has real solutions. For this reason, we'll calculate the discriminant of the equation.

delta = b^2 - 4ac, where ab,c, are the coefficients of the equation:

ax^2 + bx + c = 0

We'll identify a,b,c:

a = 2

b = 6

c = 5

delta = 36 - 40 = -4 < 0

**Since delta is negative, then the equation has no real roots, but it has complex roots.**