Question

If (x-2 ) is a factor of the polynomial x3+2x2-13x+k then 'k' is equal to ?​

Answer 1

SOLUTION

GIVEN

( x - 2 ) is a factor of the polynomial x³ + 2x² - 13x + k

TO DETERMINE

The value of k

EVALUATION

Let f(x) = x³ + 2x² - 13x + k

Since ( x - 2 ) is a factor of the polynomial f(x)

∴ f(2) = 0

⇒ 2³ + 2 × 2² - 13 × 2 + k = 0

⇒ 8 + 8 - 26 + k = 0

⇒ k - 10 = 0

⇒ k = 10

FINAL ANSWER

Hence the required value of k = 10

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Answer 2

Answer:

Since ( x - 2 ) is a factor of the polynomial f(x)

∴ f(2) = 0

⇒ 2³ + 2 × 2² - 13 × 2 + k = 0

⇒ 8 + 8 - 26 + k = 0

⇒ k - 10 = 0

⇒ k = 10