Question

find the value of k if (x-1) is
factor of 4X²+ 3x2 - 4X+k​

Answer 1

Answer :

k = -3

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem : • If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero , ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

• If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero , ie. R = p(c) = 0 .

Solution :

Let the given polynomial be p(x) .

Thus ,

p(x) = 4x³ + 3x² - 4x + k

Also ,

If x - 1 , then x = 1 .

Also ,

It is given that , (x - 1) is a factor of given polynomial p(x) , thus the remainder obtained on dividing p(x) by (x - 1) will be zero , ie . R = p(1) = 0 .

Thus ,

=> p(1) = 0

=> 4•1³ + 3•1² - 4•1 + k = 0

=> 4 + 3 - 4 + k = 0

=> 3 + k = 0

=> k = -3

Hence k = -3 .

Answer 2

Answer:

Required Answer:-

let's understand the concept:-

• Here if x-1 is a factor of the the polynomial =>x-1=0=>x=1
• If it is a factor then p (1)=0

solution:-

$\sf {p (x)={4x}^{2}+{3x}^{2}-4x+k}$

${:}\dashrightarrow$$\sf {p(x)={7x}^{2}-4x+k}$

• According to the question

${:}\dashrightarrow$$p (1)=0$

${:}\dashrightarrow$$7 (1){}^{2}-4 (1)+k=0$

${:}\dashrightarrow$$7×1-4+k=0$

${:}\dashrightarrow$$7-4+k=0$

${:}\dashrightarrow$$3+k=0$

${:}\dashrightarrow$${\underline{\boxed{\bf {k=(-3)}}}}$

$\therefore$$\sf {The\:value\:of\:k=(-3)}$