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sologuitar

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Registered: 2022-09-19

Posts: 467

Real Solutions of the Quadratic Equation...B

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?

Bob

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Registered: 2010-06-20

Posts: 10,169

Re: Real Solutions of the Quadratic Equation...B

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Real Solutions of the Quadratic Equation...B

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)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Real Solutions of the Quadratic Equation...B

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.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Real Solutions of the Quadratic Equation...B

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?

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Real Solutions of the Quadratic Equation...B

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).

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Real Solutions of the Quadratic Equation...B

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.