math

1. Let α, β be the roots of the equation x2 - px + r = 0 and α/2, 2β be the roots of the equation x2 - qx + r = 0. Then the value of r is ?

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  1. "Let α, β be the roots of the equation x2 - px + r = 0"
    This implies:
    (x-α)(x-β)=0
    or
    r=αβ ...(1)
    p=α+β ...(2)

    "and α/2, 2β be the roots of the equation x2 - qx + r = 0."
    implies:
    (x-α/2)(x-2β)=0
    or
    r=αβ ...(1a)
    q=α/2+2β ...(3)

    From (2) and (3) solve for α and β in terms of p and q, hence find r=αβ

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