Question

Find the value of k for which (x-2) is a factor of ( x² + 3x+ k)

Answer 1

Answer:

k = -10

Step-by-step explanation:

Since (x - 2) is factor so it will satisfy the given equation.

Answer 2

Answer:

The value of k is - 10.

Step-by-step-explanation:

The given polynomial is x² + 3x + k.

Let the polynomial be P ( x ).

We have given that,

( x - 2 ) is a factor of the given polynomial.

By factor theorem,

If x = 2, P ( x ) = 0

∴ ( 2 )² + 3 * 2 + k = 0

⇒ 4 + 6 + k = 0

⇒ k + 10 = 0

⇒ k = - 10

∴ The value of k is - 10.

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Verification:

The given polynomial is x² + 3x + k.

We have, k = - 10.

By substituting k = - 10 in polynomial,

P ( x ) = x² + 3x - 10

⇒ P ( x ) = x² + 5x - 2x - 10

⇒ P ( x ) = x ( x + 5 ) - 2 ( x + 5 )

⇒ P ( x ) = ( x - 2 ) ( x + 5 )

∴ ( x - 2 ) is a factor of the polynomial x² + 3x + k when k = - 10.

Hence verified!