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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

Show that the real solutions of the equation ax^2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx^2 + bx + a = 0. Assume that b^2 - 4ac is greater than or equal to 0.

Any hints? What is the first step to consider?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,503

I've written down the solutions using the quadratic formula, let's say x and x' for the first and y and y' for the second.

To be reciprocals x times y (or maybe y') must equal 1 and similarly x' with y' or y

Haven't tried it yet but I think it should work.

edit: tried it now. It does if you do x times y' (in other words take the plus root for one with the minus root of the other ... then loads of canceling, leaving 4ac/4ac = 1).

Bob

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**amnkb****Member**- Registered: 2023-09-19
- Posts: 253

sologuitar wrote:

Show that the real solutions of the equation ax^2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx^2 + bx + a = 0. Assume that b^2 - 4ac is greater than or equal to 0.

Just answer the questions posted and keep your text math-related.

*Last edited by amnkb (2023-11-16 18:23:04)*

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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

Bob wrote:

I've written down the solutions using the quadratic formula, let's say x and x' for the first and y and y' for the second.

To be reciprocals x times y (or maybe y') must equal 1 and similarly x' with y' or y

Haven't tried it yet but I think it should work.

edit: tried it now. It does if you do x times y' (in other words take the plus root for one with the minus root of the other ... then loads of canceling, leaving 4ac/4ac = 1).

Bob

The wording in this application is horrible.

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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

amnkb wrote:

sologuitar wrote:Show that the real solutions of the equation ax^2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx^2 + bx + a = 0. Assume that b^2 - 4ac is greater than or equal to 0.

Just answer the questions posted and keep your text math-related.

Again, what data in the application led you to work out the problem as you did? You said (1/r) is a solution to the quadratic equation given. When you say "a solution", do you mean there are more solutions?

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**KerimF****Member**- From: Aleppo-Syria
- Registered: 2018-08-10
- Posts: 209

sologuitar wrote:

When you say "a solution", do you mean there are more solutions?

As you know, in general, a quadratic equation has two roots (real or complex) if (b^2 - 4ac) ≠ 0. We may say that 'r' is one of them (for known a, b and c).

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).

But only a human may have the freedom and ability to oppose his natural robotic nature.

But, by opposing it, such a human becomes no more of this world.

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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

KerimF wrote:

sologuitar wrote:When you say "a solution", do you mean there are more solutions?

As you know, in general, a quadratic equation has two roots (real or complex) if (b^2 - 4ac) ≠ 0. We may say that 'r' is one of them (for known a, b and c).

Much better this time. Less lectures and philosophy and more mathematics.

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