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maths

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if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of
(i)alpha^2+beta^2
(ii)1/alpha^2+1/beta^2
(iii)(r)alpha/beta+(r)beta/alpha
(iv)alpha^-1+beta^-1

  • maths - ,

    The general solution to the equation
    ax^2+bx+c=0
    is, using the quadratic formula:
    α=(-b+√(b²-4ac))/2a, and
    β=(-b-√(b²-4ac))/2a

    From there, expand α²+β² to get (b²-2ac)/a²

    I will leave parts (ii) to (iv) for you as practice.

  • maths - ,

    alpha+beta=-b/a
    =--4/2
    =2
    alpha^2+beta^2=(alpha+beta)^2
    =2^2
    =4

    (ii)take reciprocal(1/2)^2=1/4
    (iv)a^-1=1/a similarly 1/2

    tried my best to answer hope its correct:)
    your pal
    mathew

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