SOLUTION: Solve the quadratic inequality. Write the solution set in interval notation and show the complete solution.
2𝑥^2≤5𝑥−2
Question 1087726: Solve the quadratic inequality. Write the solution set in interval notation and show the complete solution.
2𝑥^2≤5𝑥−2 Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Critical x values are at .
The quadratic expression will be BELOW 0 between and .
For the "... equal to" part, the two values are included.
Interval Notation: [ 1/2, 2 ]
<= .
Move the terms from the right side to the left, changing the signs. You will get an equivalent inequality
<= 0.
Factor the left side:
(2x-1)*(x-2) <= 0.
Divide both sides by 2. You will get an equivalent inequality
(x-1/2)*(x-2) <= 0. (1)
1) If x < then both factors (each factor) in the left side of (1) are/is negative,
So the product is positive.
2) If < x < 2 then the factor (x-1/2) is positive, while the factor (x-2) in the left side of (1) is negative,
so the product is negative.
3) If 2 < x then both factors (each factor) in the left side of (1) are/is positive,
so the product is positive.
Answer. The given inequality has the segment [1/2,2] as the solution set.
(