11.07 Quadratic inequalities
Interactive practice questions
Consider the inequality $x^2-3x-10\ge0$x2−3x−10≥0.
First factor $x^2-3x-10$x2−3x−10.
For what values of $x$x is $x^2-3x-10=0$x2−3x−10=0? Leave your solutions on the same line separated by a comma.
To solve the inequality, Micky splits up the entire number line into three intervals, and tests a value from each interval to see if it satisfies the inequality $x^2-3x-10\ge0$x2−3x−10≥0.
| Interval A ($x<-2$x<−2) | $x=-2$x=−2 |
Interval B ($-2 |
$x=5$x=5 | Interval C ($x>5$x>5) |
| Value to test | Value to test | Value to test | ||
| $x=-3$x=−3 | $x=1$x=1 | $x=7$x=7 |
Which values of $x$x satisfy the inequality $x^2-3x-10\ge0$x2−3x−10≥0? Select all that apply.
$x=7$x=7
$x=-3$x=−3
$x=1$x=1
Hence, state the solution to the inequality $x^2-3x-10\ge0$x2−3x−10≥0. You may use the keywords "and"/"or".
Consider the inequality $4x^2-12x+9\le0$4x2−12x+9≤0.
Solve the inequality $\left(1-x\right)\left(x-4\right)\ge2$(1−x)(x−4)≥2.
Solve the inequality $2x+8-3x^2\le0$2x+8−3x2≤0. You may use the keywords "and"/"or".