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Answer 1

1

Secondary School

Math

10 points

If polynomial 2x 4 + 3x 3 + 2kx 2 +3x+6 is exactly divisible by (x+2) then value of k is: Could you plz tell it in detail fast.

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 byN1askoasrirose 05.06.2016

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tanu35 

Helping Hand

P (x)=x+2

p (x)=0

0=x+2

-2=x

we put -2 in the place of x

p (x)= 2x 4+ 3x 3+2kx2+3x+6

p (x)=0

0= (2×-2×4)+(3×-2×3)+(2×k×-2×2)+(3×-2)+6

0=-16+(-18)+(-8k)+(-6)+6

0=-16-18-8k-6+6

0=-34-8k

0+34=8k

34=8k

34/8=k

17/4=k

Answer 2

Solution:-

Given:-

• Polynomial :- ( 2x⁴ + 3x³ + 2kx² + 3x + 6)
• ( x + 2) is the Factor.

To Find:-

• value of k = ?

Find:-

∵ ( x + 2 ) is the Factor.

=) x + 2 = 0

=) x = -2

P(x) = 2x⁴ + 3x³ + 2kx² + 3x + 6

=) P(-2) = 2(-2)⁴ + 3(-2)³ + 2k(-2)² + 3(-2) + 6

=) 0 = 2(16) + 2(-8) + 2k(4) - 6 + 6

=) 0 = 32 - 16 + 8k

=) 8k = 16 - 32

=) 8k = -16

=) k = -2

Hence,

k takes the value of (-2).