Question

I find the value of m and in the polynomial
2 x² + mx ² + nx -14 such that (x-1) and (x+2)
are its factors,​

Answer 1

Answer:

Givan that

2x²+mx²+nx-14 and

x-1=0

x=1 and

x+2=0

x=-2

naw,

accourding to question:-

if x=1 than

2+m+n-14=0

⇒m+n=12 ............(1)

again,

when x=-2 than

8+4m-2n-14=0

⇒2m-n=6............(2)

naw add equation 1 and 2 tha we get:-

m+n=12

+2m-n=6

⇒3m=18

m=6 and

⇒m+n=12

⇒6+n=12

n=6

therefore the value of m and n is 6 and 6.

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

p(x)=2x^2+mx^2+nx-14

p(1)=2(1^2)+m(1^2)+n(1)-14=0

2+m+n-14=0

m+n=12---(1)

p(-2)=2(-2^2)+m(-2^2)+n(-2)-14=0

8+4m-2n-14=0

4m-2n=6

2m-n=3--(2)

(1)+(2)

3m=15

m=5

substitute in (1)

n=7