Question

3)
The value of k if
(° + x)
(3x² + 2x + k) = 0 is​

Answer 1

Answer:

We know that is is possible to factor a polynomial using its roots. For a quadratic polynomial this means that we can write it as (x−r1)(x−r2). In this case we have the roots 2 and 3 meaning the polynomial can be written as:

(x−2)(x−3)=x2−3x−2x+6=x2−5x+6

The above equation is equivalent to the on given in the problem. To compare the two we multiply the above equation through by three getting:

3x2−15x+18

Comparing that to 3x2−2kx+2m we see that −2km=−15 making k=152 , we also see that 2m=18 making m=9 .

This is a good example of the fact that it can come in handy to know several ways of finding roots in polynomial equations. Had one only known what I would call the standard formula for finding roots in quadratic equations this would have been a mess to solve

(I am talking about the formula r=−b±d−−√2a where d=b2−4ac )

Step-by-step explanation: