Previous year IIT jee Question
Chapter :- complex number and quadratic equation
Answers
Step-by-step explanation:
correct option is (A) Go for it
Hope it is helpful pls mark me as brainliest
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.