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

Aug 1, 2016

Closed interval $\left[- 1 , \frac{7}{2}\right)$

#### Explanation:

Bring the quadratic inequality to standard form:
$f \left(x\right) = 2 {x}^{2} - 5 x - 7 \le 0$
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
$x 2 = - \frac{c}{a} = \frac{7}{2}$
Answer by closed interval $\left[- 1 , \frac{7}{2}\right]$. The 2 end points are included.