Question

one root of the equations x²-5x+k=0 is 2 then find the value of k​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• One root of the equations x²-5x+k=0 is 2.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The value of k .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

We have,

f(x) = x² - 5x + k = 0

One root of the equations x²-5x+k=0 is 2.

Such that , f(x) = 2

➝ f (x) = x² - 5x + k = 0

➝ f (2) = 2² - 5(2) + k = 0

➝ 2 × 2 - 5× 2 + k = 0

➝ 4 - 10 + k = 0

➝ - 6 + k = 0

➝ k = 6

$\sf{\huge{\underline{\green{Verification :-}}}}$

x²-5x+k=0

k = 6

➝ 6²- 5 × 6 + 6 = 0

➝ 36 - 30 + 6 = 0

➝ 36 - 36 = 0

➝ 0 = 0

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