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# Is pq > 0? (1) x^2 - px + q = 0 has real and positive roots

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VP
Joined: 23 Feb 2015
Posts: 1258
Is pq > 0? (1) x^2 - px + q = 0 has real and positive roots  [#permalink]

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07 Apr 2019, 08:46
2
00:00

Difficulty:

75% (hard)

Question Stats:

36% (01:49) correct 64% (02:31) wrong based on 44 sessions

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Is pq > 0?

(1) x^2 - px + q = 0 has real and positive roots

(2) p(p - q) > 0

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Joined: 27 May 2012
Posts: 902
Is pq > 0? (1) x^2 - px + q = 0 has real and positive roots  [#permalink]

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07 Jun 2019, 03:07
1
Is pq > 0?

(1) x^2 - px + q = 0 has real and positive roots

(2) p(p - q) > 0

let $$x_1$$ and $$x_2$$ be the roots of the quadratic , given both are positive.
also sum of roots of a quadratic$$\>$$ $$x_1+x_2=-(\frac{-p}{1}) \Rightarrow x_1+x_2=p$$
Product of roots$$\>$$$$x_1*x_2=q$$
since $$x_1$$ and $$x_2$$ both are positive hence p and q are also positive.Hence pq>0

Ans A
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Re: Is pq > 0? (1) x^2 - px + q = 0 has real and positive roots  [#permalink]

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07 Apr 2019, 10:20
1.
p²-4q>O
p²>4q
but cant say about q's sign.
so, insufficient

2. p²-pq>O
p²>pq
p² will always be positive.
hence sufficient.

IMO B

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Re: Is pq > 0? (1) x^2 - px + q = 0 has real and positive roots   [#permalink] 07 Apr 2019, 10:20
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