Question

if x-1 and x+2 are factors of polynomial 2x^3+mx^2-x-n then value of m^2+n^2 is

Answer 1

Answer: 61

Step-by-step explanation:

Since (x−1) is a factor of given polynomial.

∴x=1 will satisfy the given equation.

Let, f(x)=2x3+mx2−x−n

Then f(1)=0

⇒2+m−1−n=0

or, m−n=−1..........(1)

Also (x+2) is a factor of f(x).

∴x=−2 will satisfy the given equation.

Then f(−2)=0

⇒−16+4m+2−n=0

⇒4m−n=14........(2)

From (1) and (2) we get, m=5 and n=6.

Now, m2+n2

=5^2+6^2

=25+36

=61.