Question

-2х^2-5х+3больше равно 0

Answer 1

D=(-5)²-4•(-2)•3=25+24=49=7²
X1,2=5±7/4
X1,2=3и -0,5

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-------•-----------•-------->x
-0,5. 3
Ответ:[-0,5;3]
Вроде так(сорян,фото не получилось загрузить)

Answer 2

To solve the inequality, you need to find the values of x for which the expression -2x^2 - 5x + 3 is greater than or equal to 0.

Step 1: Find the roots of the quadratic equation -2x^2 - 5x + 3 = 0: To do this, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

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

x = (5 ± √((-5)^2 - 4 * -2 * 3)) / (2 * -2) x = (5 ± √(25 + 24)) / -4 x = (5 ± √49) / -4 x = (5 ± 7) / -4

So the roots of the equation are x = (-5 + 7) / -4 = -1/2 and x = (-5 - 7) / -4 = 3.

Step 2: Analyze the inequality: The inequality -2x^2 - 5x + 3 ≥ 0 means that we want to find the regions where the expression is greater than or equal to zero.

Step 3: Create a sign chart or use test points: To determine the regions where the expression is positive or negative, you can use test points within each interval and evaluate the expression at those points. You can also use a sign chart to do this.

Testing a point within each interval: Let's test x = 0, x = -1, and x = 4.

For x = 0: -2(0)^2 - 5(0) + 3 = 3 > 0

For x = -1: -2(-1)^2 - 5(-1) + 3 = 6 > 0

For x = 4: -2(4)^2 - 5(4) + 3 = -39 < 0

Step 4: Interpret the results: From the tests above, we can see that the expression -2x^2 - 5x + 3 is greater than 0 in the intervals (-∞, -1/2) and (0, 3]. It is less than 0 in the interval [-1/2, 0) and (3, +∞).

Step 5: Write the final solution: The inequality -2x^2 - 5x + 3 ≥ 0 is true when x is in the intervals (-∞, -1/2] and (0, 3].

In interval notation, the solution is: x ∈ (-∞, -1/2] ∪ (0, 3].