Question

please answer my question tennetiraj sir​

Answer 1

Answer:

d is the correct ans

i hope half you

Mark me brainlist

Answer 2

Option C

Step-by-step explanation:

Given :-

2x⁴-2x³+3kx²-10x+14 and 2x³+kx²+2x+4 are divided by (x-1) then remainders are same.

To find :-

Find the value of k ?

Solution :-

Given polynomials are 2x⁴-2x³+3kx²-10x+14 and 2x³+kx²+2x+4

Let p(x) = 2x⁴-2x³+3kx²-10x+14

Let g(x) = 2x³+kx²+2x+4

Given divisor = (x-1)

We know that

Remainder Theorem

If P(x) is divided by (x-a) then the remainder is P(a).

Given p(x) and g(x) are divided by (x-1) then the remainders are p(1) and g(1)

Put x= 1 in p(x) then

=> p(1)= 2(1)⁴-2(1)³+3k(1)²-10(1)+14

=> p(1) = 2(1)-2(1)+3k(1)-10+14

=> p(1) = 2-2-+3k-10+14

=> p(1) = 16-12+3k

=> p(1) = 4+3k---------(1)

Put x = 1 in g(x) then

=>g(1) = 2(1)³+k(1)²+2(1)+4

=> g(1) = 2(1)+k(1)+2+4

=> g(1) = 2+k+2+4

=> g(1) = 8+k ----------(2)

Given that

The remainders are same

=> p(1) = g(1)

=> (1)=(2)

=> 4+3k = 8+k

=> 3k-k = 8-4

=>2k = 4

=> k = 4/2

=> k = 2

Therefore, k = 2

Answer:-

The value of k for the given problem is 2

Used formulae:-

Remainder Theorem:-

Let P(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial if P(x) is divided by (x-a) then the remainder is P(a).