Thread: Verify Each Given Statement

See picture.

2. Re: Verify Each Given Statement

We can't give "steps" that will lead you to a solution without know what you can do or understand about these problems. And we could best learn this by seeing what you have attempted yourself. Do you, for example, know that if $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of $\displaystyle ax^2+ bx+ c= 0$ the $\displaystyle ax^2+ bx+ c= a(x- \alpha)(x- \beta)$? Do you know the quadratic formula?

3. Re: Verify Each Given Statement

Can you please verify the first-two questions? I can then use your steps or solution to answer parts 3 and 4.

4. Re: Verify Each Given Statement

What is $\displaystyle \dfrac{-b+\sqrt{b^2- 4ac}}{2a}+ \dfrac{-b- \sqrt{b^2- 4ac}}{2a}$?

What is $\displaystyle \left(\dfrac{-b+\sqrt{b^2- 4ac}}{2a}\right)\left(\dfrac{-b- \sqrt{b^2- 4ac}}{2a}\right)$?

That is exactly what this problem is asking you to do. Why have you not done it?

(You do know that $\displaystyle (a- b)(a+ b)= a^2- b^2$, don't you?)

5. Re: Verify Each Given Statement

Thank you. I am at the job right now. Monday is my next day off. I will work it out on Monday and post my answer here. Math is fun, honestly. To think that I do this just for fun. I am not in any class.