1.2 x^2 - 1.3 x - 5.5
Which values of x, to two decimal places, satisfy the inequality? The answer is -1.67<x<2.75 How do I solve this?
Could I use a graphing calculator so I can solve for these? I must have two answers.
1.2 x^2 - 1.3 x - 5.5
Which values of x, to two decimal places, satisfy the inequality? The answer is -1.67<x<2.75 How do I solve this?
Could I use a graphing calculator so I can solve for these? I must have two answers.
It was probably "find all x for which $\displaystyle 1.2x^2- 1.3x- 5.5< 0$". Using a graphing calculator, you graph $\displaystyle y= 1.2x^2- 1.3x- 5.5$ (I used the one at https://www.desmos.com/calculator). Notice that parabola goes below the x-axis and, if necessary use the zoom feature to determine that the parabola crosses the x-axis at "x= -1.667" (which is probably -5/3) and at "x= 2.75" (11/4). We can check that "probably" by setting x= -5/3 in the inequality- 1.2(25/9)- 1.3(-5/3)- 5.5= 0.
Or you could use the quadratic formula to determine the endpoints of the interval: $\displaystyle x= \frac{1.3\pm\sqrt{1.3^2- 4(1.2)(5.5)}}{2(1.2)}= \frac{1.3\pm\sqrt{28.09}}{2.4}= \frac{1.3\pm 5.3}{2.4}$.