Question

find the values of m and n in the polynomial 2x³+mx²+nx-14 such that (x-1) and (x+2) are its factors​

Answer 1

Answer:

Step-by-step explanation:

Given that,

f(x)=2x  

2

+mx  

2

+nx−14

(x−1)and(x+2) Factor at f(x)

x−1=0

⇒x=1

x+2=0

⇒x=−2

f(x)=2×1  

3

+m×1  

2

+1n−14

f(−2)=0

2(−2)  

3

+m(−2)  

2

+n(−2)−14=0

⇒0=2+m+n−14

⇒m+n=12−−−−(1)

−16+4m−2n=0

4m−2n−30=0

2(2m−n)=30

2m−n=15−−−−−(2)

on solving (i) & (ii) we get

m+n=12

2m−n=15

3m=27

 

m=  

3

27

​

 

m=9

Now put m=9 in eqn(i) we have

⇒m+n=12

⇒9+n=12

⇒n=3

So,

n

m

​

=  

3

9

​

=3