Solve 3x² + 2x + 7 = 0. Round solutions to the nearest hundredth.

Solution:

A quadratic equation is an algebraic expression of the second degree in x.

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

Where a, b are the coefficients,

x is the variable, and

c is the constant term.

Given, the equation is 3x² + 2x + 7 = 0

We have to find the solutions of the equation.

Using the quadratic formula,

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Here, a = 3, b = 2 and c = 7

\(x=\frac{-2\pm \sqrt{(2)^{2}-4(3)(7)}}{2(3)}\\=\frac{-2\pm \sqrt{4-84}}{6}\\=\frac{-2\pm \sqrt{-80}}{6}\)

Since there is a negative element under the square root, there are no real solutions.

Therefore, there are no real solutions to the given equation.

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Solve 3x² + 2x + 7 = 0. Round solutions to the nearest hundredth.

Summary:

The equation 3x² + 2x + 7 = 0 has no real solution.