Math, asked by prachithaman1, 1 year ago

please tell me how to factorise this equation

Attachments:

Answers

Answered by VedaantArya

By observation, three of the roots are: 1, -1, -2.

Let the fourth root be z.

Since the sum of roots is -b/a = -5, so:

z + 1 - 1 - 2 = -5

z = -3

So, the roots are: 1, -1, -2, -3.

Hence, the factorized equation is: (x - 1)(x + 1)(x + 2)(x + 3)

vishalkumar2806: where do you get this amazing observation

VedaantArya: I saw a -5 and a -6 at the end, a +1, +5 and another +5 at the beginning. +1, +5 collectively cancel out the -6 and the other +5, the -5. So, if there was no role of x, that is, x = 1, the equation is satisfied.
A quick glance over the coefficients of x^3 and x -> they're cancelling each other (+5, -5), so interchanging signs won't mess anything with x = 1, so x = -1 is also a root.

VedaantArya: With a tiny leap of faith, I felt putting -2 would cancel out stuff, since the coefficient of x^3 was positive and much larger than that of x^4 -> so maybe (just maybe) it'll somehow fit.
And it did.

So there.

vishalkumar2806: Amazing Man..

vishalkumar2806: Wondeefull

Previous Question

Next Question

please tell me how to factorise this equation​

Answers

please tell me how to factorise this equation