Current Year 12 Thread Mark VI

Good luck I'm sure you'll get 101%

Also $\displaystyle \sum_{i=1}^n ( a_i x +b_i )^2$

Determine the conditions for the roots of the quadratic in x.

Good luck!

Thanks.

Withdrawal symptoms from not going on skype. Must. Refrain.

Let the games maths begin.

The Complete University Guide

Do you want the list from Mark V?

If so:

Also $\displaystyle \sum_{i=1}^n ( a_i x +b_i )^2$

Determine the conditions for the roots of the quadratic in x.

So far I have:

$(a_1b_1+a_2b_2+a_3b_3+\cdots +a_nb_n)^2 \geq (a_1^2+a_2^2+a_3^2 + \cdots + a_n^2)(b_1^2+b_2^2+b_3^2 + \cdots + b_n^2)$

Upon multiplying out and saying that the discriminant must be greater than or equal to zero, then simplifying and rearranging...

It looks like the Cauchy-Schwarz inequality but with the inequality sign the other way round.

Distance equals speed times time, not the other way round. Silly me.

Part one done!

The inequality is the wrong way around....

What makes you think the roots are real?

Damnit...

I dunno actually... I sort of made an assumption there, didn't I?

Well. We know that the function is always equal or greater than one, so what does this imply about the roots?

Also $\displaystyle \sum_{i=1}^n ( a_i x +b_i )^2$

Determine the conditions for the roots of the quadratic in x.

$(a_1b_1+a_2b_2+a_3b_3+\cdots +a_nb_n)^2 < (a_1^2+a_2^2+a_3^2 + \cdots + a_n^2)(b_1^2+b_2^2+b_3^2 + \cdots + b_n^2)$

Thanks for the hint.

You are welcome.

Don't do it!

I thought that proof was rather nice

Ok... now I will start with maths