About k^2+k-6

Question

We know that k^2+k-6 = (k-3)(k+2)

I see that we are diving "-6" into "+/-3" times "+/-2". However, can anyone tell me why is it "-3 and 2", instead of "3 and -2"?

Thanks!

preeti95 · Answer

Your factorisation is wrong.

k^2+k-6 = k^2+(3k-2k)-6 = (k+3)(k-2)

Hence, roots of the equation are -3 and +2

CrackverbalGMAT · Answer

When finding the roots of the quadratic equation a x^2  + bx + x = 0, using the method of splitting the middle term into 2 parts, then

(i) The sum of the middle terms should be = b

(ii) The product of the middle terms should be ac

In  k^2  + k - 6, the split should happen such that the sum of the terms = 1 and the product of the terms = 1*-6 = -6

Therefore the middle terms should be +3k and -2k

We get  k^2  + 3k - 2k - 6 = 0

k(k + 3) - 2(k + 3) = 0

(k + 3)(k - 2) = 0

The roots are therefore -3 and 2

Hope This Helps

Arun Kumar

globaldesi · Answer

You can take out smaller power only as common.
example
 X^2 +x^3 
can be written as  x^2(x+1) 
similarly -6 is smaller hence common out

graceo · Answer

Thank you!! This makes so much sense:)

graceo · Answer

Yup I realized lol...thank you!

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