Answer:
The negative root is between -3 and -2.
Step-by-step explanation:
The roots of a quadratic equation are the x values that make y zero, that is, the places where the graph intersects the x axis. There are two roots, the negative perhaps -2.5 and the positive between 1 and 1.5. So, the negative root is between -3 and -2.
Answer:
Step-by-step explanation:
bsolutely, let's graph the function and analyze the roots:
Graphing the function:
Go to your graphing calculator and access the function mode (usually by pressing the "Y=" key or a similar function button).
Enter the function equation: f(x) = 5x^2 + 6x - 17
Set the viewing window to a range that allows you to see the behavior of the parabola clearly. A good starting point could be something like Xmin=-5, Xmax=5, Ymin=-30, Ymax=30 (this can be adjusted based on the calculator's output).
Graph the function.
Analyzing the Roots:
By looking at the graph of the function, we can determine the following about the roots:
The parabola intersects the x-axis at two points, indicating there are two roots.
Using the calculator to find the exact roots:
Most graphing calculators have a feature to find the roots or zeros of a function. Look for a function like "ZERO" or "X-solve." Following the specific instructions for your calculator model, you can find the exact values of the roots.
Common calculator methods to find roots:
TI-84 series: Press "2nd," then "CALC," and choose "ZERO." Enter the function expression f(x) and press ENTER a few times to see both roots.
Casio fx-series: Press "SHIFT" and "CALC," then select "0" (Zero). Enter the function expression f(x) and press ENTER a few times to see both roots.
Once you have the exact root values, you can determine which statement is true based on their location.
In conclusion, analyzing the graph or using the calculator to find the exact roots will reveal that the statement about the roots being between 0 and 1 is not necessarily true. There might be other possibilities depending on the specific values of the roots.