Complex Numbers And Quadratic Equations

Question
CBSEENMA11015598

If the difference between the roots of the equation x2 + ax + 1 = 0 is less than 5 , then the set of possible values of a is

  •  (−3, 3)

  • (−3, ∞)

  • (3, ∞)

  • (−∞, −3)

Solution

A.

 (−3, 3)

D.

(−∞, −3)

x2 + ax + 1 = 0
α + β = −a αβ = 1
vertical line straight alpha space minus straight beta vertical line space equals space square root of left parenthesis straight alpha space plus straight beta right parenthesis squared space minus 4 αβ end root
vertical line straight alpha minus straight beta vertical line space equals space square root of straight a squared minus 4 end root
square root of straight a squared minus 4 end root space less than square root of 5
straight a squared space minus space 4 less than 5
straight a to the power of 2 minus end exponent space 9 less than 0
straight a element of space left parenthesis negative 3 comma 3 right parenthesis

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