if 4x³ + 8x² - x - 2 = 0 then the value
of (2x + 3) is given by
since there are three values of x which satisfy the equation, there are three values for 2x+3.
jknk
To find the value of (2x + 3) when the equation 4x³ + 8x² - x - 2 = 0 is satisfied, we need to solve the given equation first.
Step 1: Start with the given equation: 4x³ + 8x² - x - 2 = 0
Step 2: To solve this equation, we can try using factoring, the quadratic formula, or synthetic division. In this case, let's use factoring.
Step 3: Group the terms in pairs to see if there are any common factors. In this case, we can group the first two terms and the last two terms:
4x³ + 8x² - x - 2 = (4x³ + 8x²) - (x + 2)
Step 4: Factor out the common terms from each group:
4x²(x + 2) - 1(x + 2) = (4x² - 1)(x + 2)
Step 5: Now, we have factored the equation to (4x² - 1)(x + 2) = 0.
Step 6: Set each factor equal to zero and solve for x:
4x² - 1 = 0 or x + 2 = 0
For the first equation, we can add 1 to both sides and then take the square root:
4x² = 1
x² = 1/4
x = ±√(1/4)
x = ±1/2
For the second equation, we simply subtract 2 from both sides:
x + 2 = 0
x = -2
Step 7: Now that we have the possible values of x, we can substitute these values into the expression (2x + 3) to find the corresponding values:
When x = -2, (2x + 3) = 2(-2) + 3 = -4 + 3 = -1
When x = 1/2, (2x + 3) = 2(1/2) + 3 = 1 + 3 = 4
Therefore, the value of (2x + 3) is -1 or 4, depending on the value of x.