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प्रश्न
If the roots of the equation q2x2 + p2x + r2 = 0 are the squares of the roots of the equation qx2 + px + r = 0, then q, p, r are in __________
पर्याय
A.P.
G.P.
Both A.P. and G.P.
none of these
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उत्तर
G.P.
Explanation;
Hint:
q2x2 + p2x + r2 = 0
Let the roots be α2 + β2
α2 + β2 = `(−"p"^2)/("q"^2)`
α2β2 = `("r"^2)/("q"^2)`
qx2 + px + r = 0
Let the root be α and β
α + β = `(-"p")/("q")`, αβ = `"r"/"q"`
α2 + β2 = (α + β)2 – 2αβ
`(-"p"^2)/("q"^2) = "p"^2/"q"^2 - (2"r")/"q"`
`(-"p"^2)/("q"^2) - ("p"^2)/("q"^2) = - (2"r")/"q"`
`(-"p"^2 - "p"^2)/("q"^2) = - (2"r")/"q"`
`(- 2"p"^2)/"q"^2 = - (2"r")/"q"`
p2q = q2r
p2 = qr
`"p"/"q" = "r"/"p"`
∴ q, p, r, in G.P.
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