Write expressions for two roots of the quadratic equation

[mikhailmcinally1]

Hello,

I am stuck on this homework problem, it is written bellow:


a.) Considering the quadratic formula write expressions for the two roots of the quadratic equation
ax^2 + bx + c = 0

I don't understand what it means by writing an expression for the two different roots? I've included the rest of the question below (in bold) in case it helps clarify anything

b.) add the expressions. How is this sum related to the coefficients of the quadratic equation?

c.) Multiply the expressions. How is this product related to the coefficients of the quadratic equation?

d.) Use the results from parts b and c to write and equation whose roots are x = -3 +- (11)^1/2


Thank you in advance for looking at my post

 

[Deleted member 4993]

Hello,
I am stuck on this homework problem, it is written bellow:
a.) Considering the quadratic formula write expressions for the two roots of the quadratic equation
ax^2 + bx + c = 0
I don't understand what it means by writing an expression for the two different roots? I've included the rest of the question below (in bold) in case it helps clarify anything

b.) add the expressions. How is this sum related to the coefficients of the quadratic equation?

c.) Multiply the expressions. How is this product related to the coefficients of the quadratic equation?

d.) Use the results from parts b and c to write and equation whose roots are x = -3 +- (11)^1/2
Thank you in advance for looking at my post

What is the definition of a root of a polynomial function?

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Please share your work/thoughts about this assignment.

 

[JeffM]

What does [MATH]\pm[/MATH] mean? what is the quadratic formula?

 

[Steven G]

I think that this one can be given to the student--at least part a.

The first root is [math] x = \dfrac{-b+\sqrt{b^2-4ac}}{2a}[/math]
The 2nd root is [math] x = \dfrac{-b+\sqrt{b^2-4ac}}{2a}[/math]
Now you do the rest and remember the results from b and c.

 

[JeffM]

I think that this one can be given to the student--at least part a.

The first root is [math] x = \dfrac{-b+\sqrt{b^2-4ac}}{2a}[/math]
The 2nd root is [math] x = \dfrac{-b+\sqrt{b^2-4ac}}{2a}[/math]
Now you do the rest and remember the results from b and c.

Jomo means

[MATH]\text {I: } x = \dfrac{-b + \sqrt{b^2 - 4ac}}{2a}, \text { or} \\ \text {II: } x = \dfrac{- b - \sqrt{b^2 - 4ac}}{2a}.[/MATH]

 

[Deleted member 4993]

Jomo means

[MATH]\text {I: } x = \dfrac{-b + \sqrt{b^2 - 4ac}}{2a}, \text { or} \\ \text {II: } x = \dfrac{- b - \sqrt{b^2 - 4ac}}{2a}.[/MATH]

Or sometimes those two statements (above) are combined and written as:


[MATH] x_{1,2} = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/MATH]

 

[Dr.Peterson]

a.) Considering the quadratic formula write expressions for the two roots of the quadratic equation
ax^2 + bx + c = 0

I don't understand what it means by writing an expression for the two different roots? I've included the rest of the question below (in bold) in case it helps clarify anything

b.) add the expressions. How is this sum related to the coefficients of the quadratic equation?

c.) Multiply the expressions. How is this product related to the coefficients of the quadratic equation?

d.) Use the results from parts b and c to write and equation whose roots are x = -3 +- (11)^1/2

Please note the wording: "write expressions for the two roots". They are asking for two expressions, one for each root. This is what you were given in post #5.

Now you can continue with the next step, adding those two expressions together, and so on. (There is also a very different way to obtain the same result, but this is what they want you to do.)