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# If a > 0 and b < 0, which of the following statements are true about

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Math Expert
Joined: 02 Sep 2009
Posts: 58347
If a > 0 and b < 0, which of the following statements are true about  [#permalink]

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27 May 2019, 02:32
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Difficulty:

55% (hard)

Question Stats:

42% (01:39) correct 58% (01:47) wrong based on 31 sessions

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If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation x^2 – ax + b = 0?

I. They have opposite signs.
II. Their sum is greater than zero.
III. Their product equals –b.

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

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Re: If a > 0 and b < 0, which of the following statements are true about  [#permalink]

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27 May 2019, 03:40
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1
Bunuel wrote:
If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation x^2 – ax + b = 0?

I. They have opposite signs.
II. Their sum is greater than zero.
III. Their product equals –b.

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

For a quadratic equation with roots (x1,x2) and equation ax^2 + bx + c=0
x1 + x2 = (-b)/a
x1 * x2= c/a

In the above case:-

x1 + x2= a >0...(1)
x1 * x2= b <0...(2)

So,
I Yes from (2)
II Yes from (1)
II No, their product is actually b. (b<0)
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Re: If a > 0 and b < 0, which of the following statements are true about  [#permalink]

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27 May 2019, 03:51
1
Bunuel wrote:
If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation x^2 – ax + b = 0?

I. They have opposite signs.
II. Their sum is greater than zero.
III. Their product equals –b.

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

For ax^2 + bx + c = 0

Sum of the roots = -b/a
Product of the roots = c/a

For given equation x^2 – ax + b = 0

Sum of the roots = -(-a)/1 = a (>0).
II is correct

Product of the roots = b/1 = b (negative)
III is incorrect
Since product is negative, the roots have to be of opposite signs.
I is correct

Option D
Re: If a > 0 and b < 0, which of the following statements are true about   [#permalink] 27 May 2019, 03:51
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