Math, asked by MiniDoraemon, 1 month ago

Previous year IIT jee Question
Chapter :- complex number and quadratic equation​

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Answers

Answered by dvchopada
0

Step-by-step explanation:

correct option is (A) Go for it

Hope it is helpful pls mark me as brainliest

Answered by amansharma264
9

EXPLANATION.

Sum of the roots of the quadratic equation,

ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ 1/α + 1/β.

⇒ 1/α² + 1/β² = - b/a.

⇒ (β² + α²)/(α²β²) = - b/a.

⇒ [(α + β)² - 2αβ]/(αβ)² = - b/a.

⇒ [(-b/a)² - 2(c/a)]/(c/a)² = - b/a.

⇒ [b²/a² - 2c/a]/(c/a)² = - b/a.

⇒ [b² - 2ac/a²]/(c²/a²) = - b/a.

⇒ [b² - 2ac]/c² = - b/a.

⇒ a(b² - 2ac) = -b(c²).

⇒ ab² - 2a²c = - bc².

⇒ ab² + bc² = 2a²c.

Divide equation by (abc), we get.

⇒ (ab²)/abc + (bc²)/abc = (2a²c)/abc.

⇒ b/c + c/a = 2a/b. - - - - - (A.P).

Their Reciprocals = c/b, b/a, a/c. - - - - - (H.P).

Option [C] is correct answer.

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