Question

If x=3 is one root of the quadratic equation p(x)= x²-2 kx-6=0, then find the value of k.
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Answer 1

I think it the answer

Answer 2

I have two solutions hope you like

given it's one root of the equation x² - 2kx - 6 = 0

one of its root x = 3
for finding the value of k put the value of x in this equation.

(3)² - 2k(3) - 6 = 0

9 - 6k - 6 = 0

6k = 3

k = 3/6

k = 1/2

hence,the value of k = 1/2


x² - 2(1/2)x - 6 = 0

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = 3 , x = -2

second answer

The given quadratic equation is

x² - 2kx - 6 = 0 ...(i)

Given that, x = 3 is a root of (i) no. equation.

Then,

(3)² - 2k (3) - 6 = 0

⇨ 9 - 6k - 6 = 0

⇨ 6k = 9 - 6

⇨ 6k = 3

⇨ k = 3/6

⇨ k = 1/2

Therefore, the value of k is 1/2.

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