- #1
Use discriminant for linear and quad. function.
In summary, Homework Statement:The Attempt at a Solution in a related similar thread had the user check their work for themselves. The user then substituted the points they found into each equation and got the result I showed.
- #2
Mastermind01
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Again you are correct. 
- #3
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Yes. Only that I have ##(-1.09 ; 1.73)## and ##(2.76 ; 13.27)##. But the path is correct.
It's always better to have exact numbers until the end and calculate the roots in a final step.
It's always better to have exact numbers until the end and calculate the roots in a final step.
- #4
Ray Vickson
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Evangeline101 said:
In thread after thread you ask "is this correct?...". That is a bad habit: as a matter of standard operating procedure you should check your answers for yourself (as you would need to do in an exam setting). Then, if you find something does not "work", you will know you have made an error somewhere, and asking for help then makes sense.
- #5
Mastermind01
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Ray Vickson said:
I agree , I have already given the OP a way to check her work in a related similar thread.
- #6
Evangeline101
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Ray Vickson said:
I understand, but can you suggest a less time consuming method than graphing, if I am doing an exam I won't have time to graph anything to check my answer. For this specific question, is there a way I can put the points back into the equation to verify, well maybe in this case I would have to graph since they are points of intersection.
Also I should be more clear when asking my question ( I will make sure to do that in future questions), in this case I would like to know if my process for part b is correct, does it make sense to use the linear equation to solve for y-values, and if so, is it because the linear equation is set equal to y?
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Ray Vickson
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Evangeline101 said:
To save time, don't graph anything; just check if your (x,y) values satisfy the requirement that they lie on both the line and the curve. That is easy: just plug in the numbers and calculate.
I have not checked your calculations for part (b), but I see that you have used the correct formulas. Again, you can check the solutions for yourself, by plugging in the numerical values and doing the calculations to see if everything works as it should.
Again: this is all just standard practice that you should get in the habit of doing.
- #8
Mark44
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Sure. You can substitute the points you found into each equation. If the point is on the graph, the equation should be a true statement.Evangeline101 said:
In your work above, you found one solution to be ##x = \frac{5 + \sqrt{133}}{6}##. The corresponding y value is ##y = \frac{15 + \sqrt{133}}{2}## If you substitute this x value into the right sides of the equations ##y = 3x^2 - 2x - 4## and ##y = 3x + 5## you should get the y value I show above. Note that the values I show are the exact values. If you approximate the x values using a calculator, the y values you get will be only as precise as the rounding you do.
Evangeline101 said:
FAQ: Use discriminant for linear and quad. function.
What is a discriminant?
A discriminant is a mathematical term used to determine the nature of the roots of a quadratic equation. It is found by taking the square root of the expression b^2-4ac, where a, b, and c represent the coefficients of a quadratic function in the form ax^2 + bx + c.
How is the discriminant used in linear functions?
The discriminant is not used in linear functions because it is only applicable to quadratic equations. Linear functions have a degree of 1, meaning they can be written in the form y = mx + b, and do not have a quadratic term.
What does the discriminant tell us about the roots of a quadratic equation?
The discriminant can tell us whether the quadratic equation has two real, two imaginary, or two equal roots. If the discriminant is positive, the equation will have two real roots. If it is negative, the equation will have two imaginary roots. And if the discriminant is equal to 0, the equation will have two equal roots.
How does the discriminant help us solve quadratic equations?
The discriminant can help us determine the number of solutions a quadratic equation has, and also the nature of those solutions. If the discriminant is positive, we can use the quadratic formula to find the two real roots. If it is negative, we know the equation has two imaginary roots. And if the discriminant is equal to 0, we can use the discriminant itself to find the two equal roots.
Can the discriminant be used in other types of functions?
The discriminant is only applicable to quadratic equations, so it cannot be used in other types of functions such as cubic or exponential functions. However, there are other methods and techniques that can be used to analyze the roots and solutions of these types of functions.