Question

(x+2)(x-3)=x+kx-6then k is

Answer 1

Answer:

I hope it help you guy , okay...

Answer 2

Answer:

The value of k is - 1.

Step-by-step-explanation:

The given equation is ( x + 2 ) ( x - 3 ) = x + kx - 6.

We have to find the value of k.

( x + 2 ) ( x - 3 ) = x + kx - 6

⇒ x ( x - 3 ) + 2 ( x - 3 ) = x + kx - 6

⇒ x² - 3x + 2x - 6 = x + kx - 6

⇒ x² - x - 6 = x + kx - 6

⇒ x² - x - 6 - x + 6 = kx

⇒ x² - 2x + 0 = kx

⇒ x² - 2x - kx = 0

⇒ x² - x - x - kx = 0

⇒ x ( x - 1 ) - x ( 1 + k ) = 0

⇒ ( x - 1 ) = 0 or ( 1 + k ) = 0

Now,

⇒( 1 + k ) = 0

⇒ 1 + k = 0

⇒ k = - 1

Now,

⇒ ( x - 1 ) = 0

⇒ x - 1 = 0

⇒ x = 1

∴ The value of k is - 1.

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Verification:

By substituting values of x & k in the LHS of the given equation, we get,

( x + 2 ) ( x - 3 )

⇒ ( 1 + 2 ) ( 1 - 3 )

⇒ 3 × ( - 2 )

⇒ - 6

∴ LHS = - 6

Now, by substituting values of x & k in the RHS of the given equation, we get,

x + kx - 6

⇒ 1 + ( - 1 ) × 1 - 6

⇒ 1 - 1 - 6

⇒ 0 - 6

⇒ - 6

∴ RHS = - 6

∴ LHS = RHS

Hence verified!