Question

If x+2 is a factor of polynomial
${x}^{2} - kx - 10$
Then value of K is:
A. 3
B. -3
C. 2
D. 1

​

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 :

Here ,

The given polynomial is ;

x² - kx - 10 .

Let the given polynomial be p(x) .

Thus ,

p(x) = x² - kx - 10

Here ,

It is given that , (x + 2) is a factor of the given quadratic polynomial p(x) .

Now ,

If x + 2 = 0 , then x = -2

Thus ,

If (x + 2) is a factor of p(x) , then x = -2 is a zero of p(x) and p(-2) = 0 .

Thus ,

=> p(-2) = 0

=> (-2)² - k(-2) - 10 = 0

=> 4 + 2k - 10

=> 2k - 6 = 10

=> 2k = 6

=> k = 6/2

=> k = 3

Hence , k = 3 .