MathematicsA quadratic equation whose one root is 2 and the sum of whose roots is zero, is

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is


  1. A
    x 2  + 4 = 0
  2. B
    x 2  – 4 = 0
  3. C
    4x 2  – 1 = 0
  4. D
    x 2  – 2 = 0  

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    Solution:

    Given,
    Assume that α be one root of the equation and β be the other root.
    It is given that for a quadratic equation α = 2 and α+β = 0.
    ⇒α+β =0 ⇒2+β =0 ⇒β =−2   The value of α = 2 and β = −2. ……(i)
    Product of zeroes
    αβ=2×−2 αβ=−4  
    Write the quadratic equation if α and β are the zeroes of the quadratic equation. ⇒ x 2 −(α+β)x+αβ =0 ⇒ x 2 −(2−2)x+(−4) =0 ⇒ x 2 −0x−4=0 ⇒ x 2 −4=0  
    Hence, the quadratic equation whose one root is 2 and the sum of whose roots is zero is x² – 4 = 0 and the correct option is 2.
     
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