Question

If x- 2 is a factor of 5x^2-kx-18 then find the value of k

Answer 1

Answer:

k = -1

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Step-by-step explanation:

p(x) = 5x^2-kx-18 = 0

g(x) = x-2 = 0

(take 2 to the other side)

      = x=2

(substitute the value of 'x')

∴p(2) = 5(2)^2-k(2)-18 = 0

p(2) = 5*4-2k-18 = 0

p(2) = 20-18-2k = 0

p(2) = 2-2k = 0

(take 2 to the other side--negative integer turns into a positive integer)

∴p(2) = -2k = -2

(take -2 to the other side--multiplication turns into division; and negative integer turns into a positive integer)

p(2) = k = -2/2

(after cancellation)

∴Answer= k = -1

Answer 2

Given: x-2, a factor of 5$x^{2}$ - kx - 18

To find: Value of k

Solution: According to the given question,

x-2 is a factor of 5$x^{2}$ - kx - 18

If x-2 is a factor of given equation, then on putting x = 2 in the equation it should become equal to 0.

Putting x = 2 in the given equation

⇒ $5(2)^{2} - k(2) - 18 = 0$

⇒ 5 x 4 - 2k -18 = 0

⇒ 20 - 2k - 18 = 0

⇒ 20 - 18 - 2k = 0

⇒ 2 - 2k = 0

2k = 2, k = 1

Hence, the value of k is 1.