Question

Решить неравенство 2x^+5x-7<0

Answer 1

Ответ в файле

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Answer 2

2x²+5x-7<0

2x²+5x-7=0    D=81     √D=9

x₁=-3,5      x₂=1      ⇒

(x+3,5)(x-1)<0

-∞_____+_____-3,5_____-_____1_____+_____+∞  

Ответ: x∈(-3,5;1).

Answer 3

To solve the inequality 2x^2 + 5x - 7 < 0, we can use a combination of factoring and sign analysis. Here's how you can do it:

Step 1: Factor the quadratic expression if possible. The equation can be factored as follows:

2x^2 + 5x - 7 = (2x - 1)(x + 7)

Step 2: Set each factor to zero and solve for x:

2x - 1 = 0 -> 2x = 1 -> x = 1/2

x + 7 = 0 -> x = -7

Step 3: Plot these points on a number line:

scssCopy code
 -∞      -7      1/2      +∞
  ------------------------------------------
     (-)     (+)      (-)     (+)

Step 4: Analyze the signs of the expression in each interval:

• When x < -7, both factors (2x - 1) and (x + 7) are negative, so their product is positive (negative * negative = positive).
• When -7 < x < 1/2, (2x - 1) is negative, but (x + 7) is positive, so their product is negative (negative * positive = negative).
• When x > 1/2, both factors are positive, so their product is positive (positive * positive = positive).

Step 5: Determine the solution to the inequality:

The inequality 2x^2 + 5x - 7 < 0 is satisfied in the interval -7 < x < 1/2.

So, the solution to the inequality is:

-7 < x < 1/2