Find the value of k, if (x −1) is a factor of p(x) in each of the following cases:
$(i) p (x) = x^{2} + x + k$
$(i i) p (x) = {2 x}^{2} + k x + \sqrt{2}$ [4 MARKS]

Open in App

Solution

Concept: 1 Mark
Application: 1 Mark each
Solution: 0.5 Mark each

$(i) p (x) = x^{2} + x + k$

$p (1) = 0$ (Using Remainder Theorem)

$p (1) = 1^{2} + 1 + k = 0$

$1 + 1 + k = 0$

$k = - 2$

$(i i) p (x) = {2 x}^{2} + k x + \sqrt{2}$

$p (1) = 0$ (Using Remainder Theorem)

$p (1) = {2 (1)}^{2} + k (1) + \sqrt{2} = 0$

$2 + k + \sqrt{2} = 0$

$k = - 2 - \sqrt{2}$

Suggest Corrections

Similar questions

Q. Find the value of k, if x-1 is a factor of p(x) in each of the following cases

p (x) = {2 x}^{2} + k x + \sqrt{2}

Q. Find the value of

k

, if

x - 1

is a factor of

p (x)

in each of the following cases:
(i)

p (x) = x^{2} + x + k

(ii)

p (x) = 2 x^{2} + k x + \sqrt{2}

(iii)

p (x) = k x^{2} - \sqrt{2} x + 1

(iv)

p (x) = k x^{2} - 3 x + k

Find the value of k, if x - 1 is a factor p(x) in each of the following cases:
(i) $p (x) = x^{2} + x + k$
(ii) $p (x) = 2 x^{2} + k x + \sqrt{2}$
(iii) $p (x) = k x^{2} - \sqrt{2} x + 1$
(iv) $p (x) = k x^{2} - 3 x + k$

Find the value of k, if (x −1) is a factor of p(x) in the following case:
$p (x) = {2 x}^{2} + k x + \sqrt{2}$

Find the value of k, if (x −1) is a factor of $p (x) = {2 x}^{2} + k x + \sqrt{2}$

Join BYJU'S Learning Program

Find the value of k, if (x −1) is a factor of p(x) in each of the following cases: (i)p(x)=x2+x+k (ii)p(x)=2x2+kx+√2 [4 MARKS]

Concept: 1 Mark Application: 1 Mark each Solution: 0.5 Mark each (i)p(x)=x2+x+k p(1)=0 (Using Remainder Theorem) p(1)=12+1+k=0 1+1+k=0 k=−2 (ii)p(x)=2x2+kx+√2 p(1)=0 (Using Remainder Theorem) p(1)=2(1)2+k(1)+√2=0 2+k+√2=0 k=−2−√2

Find the value of k, if (x −1) is a factor of p(x) in each of the following cases:
$(i) p (x) = x^{2} + x + k$
$(i i) p (x) = {2 x}^{2} + k x + \sqrt{2}$ [4 MARKS]