Question

if 2 x² - (2 + K) X + k = 0, where K is a real number then find the value of k if the roots are real and equal.

Please read the question carefully before answering you have to find the value of K not x.... And you have to use the method of class 10.

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Answer 1

Answer:

k = 2

Step-by-step explanation:

Given Quadratic Equation is 2x² - (2 + k)x + k = 0

Here, a = 2,b = -(2 + k), c = k.

Given that the roots are real and equal.

Δ = 0

∴ b² - 4ac = 0

⇒ (-2 - k)² - 4(2)(k) = 0

⇒ 4 + 4k + k² - 8k = 0

⇒ k² - 4k + 4 = 0

⇒ k² - 2k - 2k + 4 = 0

⇒ k(k - 2) - 2(k - 2) = 0

⇒ (k - 2)(k - 2) = 0

⇒ (k - 2)² = 0

⇒ k = 2.

Therefore,the value of k = 2.

Hope it helps!

Answer 2

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Hope it helps!