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/sci/ - Science & Math

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2656051 No.2656051 [Reply] [Original]

So /sci/,

If m and n represent the roots of 2x^2 - 4x - 3=0 what is the value of:

(m+n)^2

Can you explain to me how you got the answer?

>> No.2656061

If m and n represent the roots of 2x^2 - 4x - 3, can you express the original formula in terms of that m and n?

>> No.2656066

Looks like x = ( 4 +/- sqrt(16 + 24 ) ) / 4
so x = 1 +/- (1/2)sqrt(10)
so (m+n) = 1 + (blah) + 1 - (blah) = 2
so (m+n)^2 = 4

>> No.2656247

Let's do this thang. This is kind of neat.

Suppose a, b are roots. Then

c(x - a)(x - b)

is your polynomial where c is some constant, right? Yeah. That's fucking right. Let's expand this motherfucker.

c(x^2 - (a + b)x + ab)

So, holy shit, if you divide so that your highest power term has a coefficient of 1, then the MIDDLE TERM is the NEGATIVE of the SUM of your ROOTS.

In this case, it is (-4/2)^2 = 4. Faggatron.