Question

Find the value of k for which (-4)is a zero of the polynomial x square minus x-(2k+2)

Answer 1

$\large\bf\underline{Given:-}$

• -4 is a zero of polynomial x² - x -(2k + 2)

$\large\bf\underline {To \: find:-}$

• Value of k

$\huge\bf\underline{Solution:-}$

• p(x) = x² - x - (2k+2)
• Given zero = -4
• so, x = -4

◈ putting value of x = -4 in the given polynomial.

»» x² - x -2k - 2 = 0

»» (-4)² -(-4) - 2k - 2 = 0

»» 16 + 4 - 2k - 2 = 0

»» 20 - 2 - 2k = 0

»» 18 - 2k = 0

»» 2k = 18

»» k = 18/2

• ≫ k = 9

$\underline{\bf\: Verification:-}$

• p(x) = x² - x -(2k +2)

➡️ putting value of k = 9 in the given polynomial.

»» x² - x -(2×9+2)

»» x² - x - (18 + 2)

• »» x² - x - 20

Now finding zeroes of p(x) = x² - x - 20

»» x² - x - 20

»» x² + 4x - 5x - 20

»» x(x + 4) - 5(x + 4)

»» (x - 5)(x + 4)

• » x = 5 or x = -4

So, we get the same zero xv= -4 that is given in the Question .so value of k = 9 is correct.

Answer 2

Answer:

k = 9

Step-by-step explanation:

p(x) = x² - x - 2k - 2

-4 is a zero of p(x). → p(-4) = 0

p(-4) = (-4)² - (-4) - 2k - 2 = 0

16 + 4 - 2k - 2 = 0

18 - 2k = 0

2k = 18

k = 18/2

k = 9