Question

How do you solve and write the following in interval notation: `2x^2 - 5x ≥ 7`?

Answer 1

Closed interval `[-1 , 7/2)`

Explanation:

Bring the quadratic inequality to standard form:
`f(x) = 2x^2 - 5x - 7 <= 0`
The parabola graph is open upward (a > 0). Between the 2 x-intercepts (real roots), f(x) <= 0 , as a part of the parabola stays below the x-axis. Then, find the 2 x-intercepts (real roots) by solving f(x) = 0
Since a - b + c = 0, use shortcut. The 2 real roots are: x1 = -1 and
`x2 = -c/a = 7/2`
Answer by closed interval `[-1 , 7/2]`. The 2 end points are included.