Mathematics

Question

The roots of the quadratic equation _______ are x = 2 ± i.

x^2-4x-5=0
x^2+4x+5=0
x^2-4x+5=0
x^2+4x-5=0

2 Answer

  • If we solve the 3rd equation x^2-4x+5=0 its roots are
    (2 + 1) and (2 - i)

  • Answer:

    Option 3 is correct that [tex]x^2-4x+5[/tex]

    Explanation:

    To form a quadratic equation from its zeroes we have a formula which is

    [tex]x^2-(sum of zeroes)x+product of zeroes[/tex]

    Here we have been give the two zeroes  [tex]x=2+i[/tex] and [tex]x=2-i[/tex]

    substituting the values  [tex]x=2+i[/tex] and [tex]x=2-i[/tex] in the formula we will get

    [tex]x^2-{(2+i)+(2-i)}x+(2+i)(2-i)[/tex]

    After simplifying the equation we will get [tex]x^2-4x+5[/tex]      

    Since, [tex]i^2=-1[/tex]

    Therefore required equation is :[tex]x^2-4x+5[/tex]

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