Find quadratic equation through roots

Question: Given that (alpha) and (beta) are roots of the quadratic equation 6x - 3x^2 = 4, find the equation whose roots are

square root (alpha) and square root (beta)

Sum of roots = 2

Product of roots = 4/3

How do I make it such that the sum of square root (alpha) and square root (beta) can substituted using the original sum of roots and product of roots to find it's value?

Sorry, i'm not sure of how to input the math signs

Re: Find quadratic equation through roots

Quote:

Originally Posted by

**FailInMaths** Question: Given that (alpha) and (beta) are roots of the quadratic equation 6x - 3x^2 = 4, find the equation whose roots are

square root (alpha) and square root (beta)

Sum of roots = 2

Product of roots = 4/3

You know that the equation is $\displaystyle x^2-(\sqrt{\alpha}+\sqrt{\beta})x+ \sqrt{\alpha\beta}=0$

Moreover, you know the value of $\displaystyle (\sqrt{\alpha}+\sqrt{\beta})^2=\alpha+\beta+2\sqrt {\alpha\beta}$

Evaluate those.

Re: Find quadratic equation through roots

Quote:

Originally Posted by

**Plato** You know that the equation is $\displaystyle x^2-(\sqrt{\alpha}+\sqrt{\beta})x+ \sqrt{\alpha\beta}=0$

Moreover, you know the value of $\displaystyle (\sqrt{\alpha}+\sqrt{\beta})^2=\alpha+\beta+2\sqrt {\alpha\beta}$

Evaluate those.

Thanks for replying, I did tried that method, but my answer is a long string of number. 2.160246899. How do I continue from there?

Re: Find quadratic equation through roots

Quote:

Originally Posted by

**FailInMaths** but my answer is a long string of number. 2.160246899. How do I continue from there?

Frankly I don't how you get "a long string of number"

Both $\displaystyle \alpha~\&~\beta$ are rather simple complex numbers. That is part of this question I don't like.

However, assuming we use the principal square roots. I got rather simple answer.

Re: Find quadratic equation through roots

Quote:

Originally Posted by

**Plato** Frankly I don't how you get "a long string of number"

Both $\displaystyle \alpha~\&~\beta$ are rather simple complex numbers. That is part of this question I don't like.

However, assuming we use the principal square roots. I got rather simple answer.

square root (a + b +2square root (ab))

= square root (2+2(4/3))

= square root (14/3)

= 2.160246899 on calculator

I think there's something wrong with the variables of the question, I haven't learn simple complex numbers or principal square roots.

I will check it out with my teacher, thanks for your help, you can mark this as solved now