Question

-2х²+3х-5<0Поможіть будласка ​

Answer 1

Ответ:

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Answer 2

Solving the Quadratic Inequality -2x² + 3x - 5 < 0

To solve the quadratic inequality -2x² + 3x - 5 < 0, we can use the method of finding the roots of the corresponding quadratic equation and then analyzing the sign of the quadratic expression in the intervals determined by these roots.

Finding the Roots of the Quadratic Equation

The roots of the quadratic equation -2x² + 3x - 5 = 0 can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a = -2, b = 3, and c = -5.

Plugging these values into the quadratic formula, we get:

x = (-3 ± √(3² - 4*(-2)*(-5))) / (2*(-2))

Solving this equation will give us the roots of the quadratic equation, which we can then use to analyze the inequality.

Analyzing the Inequality

Once we have the roots of the quadratic equation, we can use them to determine the intervals where the inequality -2x² + 3x - 5 < 0 is satisfied. This can be done by plotting the roots on a number line and testing the inequality in the intervals between the roots.

Conclusion

By following these steps, we can find the solution to the inequality -2x² + 3x - 5 < 0 and determine the intervals for which the inequality holds true.