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# The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠  [#permalink]

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16 Jul 2017, 22:56
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Difficulty:

65% (hard)

Question Stats:

52% (01:57) correct 48% (02:37) wrong based on 44 sessions

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The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠ q). What is the value of (p + 1)(q + 1)?

(1) b − c = 2
(2) a = 3

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Math Expert
Joined: 02 Aug 2009
Posts: 7686
Re: The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠  [#permalink]

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17 Jul 2017, 02:56
Bunuel wrote:
The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠ q). What is the value of (p + 1)(q + 1)?

(1) b − c = 2
(2) a = 3

Quad equation is $$ax^2+bx+c=0$$...
SUM of roots=p+q=$$\frac{-b}{a}$$....(i)
PRODUCT of roots=pq=$$\frac{c}{a}$$...(ii)

Now (p+1)(q+1)=pq+p+q+1...
Substitute value from i and ii
$$\frac{c}{a}+\frac{-b}{a}+1=1+\frac{c-b}{a}$$

Statement I gives b-c and statement II gives value of a...
So combined
Sufficient

C
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Re: The roots of the quadratic equation ax^2 + bx + c = 0 are p and q (p ≠   [#permalink] 17 Jul 2017, 02:56
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