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Find the discriminant and the number of real roots for this equation. x^(2)+3x+8=0

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First, identify the coefficients a, b, and c in the quadratic equation ax^2 + bx + c = 0. In this case, we will say:

a = 1
b = 3
c = 8

Second, find the discriminant. In a quadratic equation, the discriminant (D) can be found using the formula D = b^2 - 4ac.

In this case, our discriminant will be:

D = b^2 -4ac
D = (3)^2 - 4 * (1) * (8)
D = 9 - 32
D = -23

So, the discriminant for the equation x^2 + 3x + 8 = 0 is -23.

Finally, we can use the discriminant to determine the number of real roots the equation has.

The value of the discriminant tells us about the roots of a quadratic equation:

- If the discriminant is greater than zero, the equation has two distinct real roots.
- If the discriminant is equal to zero, the equation has one real root (or a repeated root).
- If the discriminant is less than zero, the equation has no real roots.

In this case, our discriminant is -23, which is less than zero. Therefore, the equation x^2 + 3x + 8 = 0 has no real roots.

In summary, the discriminant of x^2 + 3x + 8 = 0 is -23 and this equation has no real roots.

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