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# Which of the following equations has two different roots?

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
Which of the following equations has two different roots?  [#permalink]

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18 Nov 2016, 01:47
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:40) correct 42% (01:35) wrong based on 202 sessions

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Which of the following equations has two different roots?

A. x^2−x+4=0
B. x^2−4x+4=0
C. x^2−3x+9=0
D. x^2−5x+5=0
E. x^2+3x+10=0

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Which of the following equations has two different roots?  [#permalink]

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Updated on: 18 Nov 2016, 03:01
1
Bunuel wrote:
Which of the following equations has two different roots?

A. x^2−x+4=0
B. x^2−4x+4=0
C. x^2−3x+9=0
D. x^2−5x+5=0
E. x^2+3x+10=0

Use the formula to find roots of the equation [-b +/- (sqrt b^2 - 4ac)]/2a
Calculating using the formula gives

A. x^2−x+4=0 imaginary roots b^2 < 4ac
B. x^2−4x+4=0 x= 2, 2 we are asked to find two different roots
C. x^2−3x+9=0 imaginary roots b^2 < 4ac
D. x^2−5x+5=0 two unique roots (5+ sqrt5) , (5- sqrt 5)
E. x^2+3x+10=0 imaginary roots b^2 < 4ac

Hence D

Bunuel how to write the formulas here.
Could you please write my formula correctly? I'm yet to get a hang of this.

Originally posted by Vinayak Shenoy on 18 Nov 2016, 02:56.
Last edited by Vinayak Shenoy on 18 Nov 2016, 03:01, edited 3 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51185
Re: Which of the following equations has two different roots?  [#permalink]

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18 Nov 2016, 02:59
Vinayak Shenoy wrote:
Bunuel how to write the formulas here.

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Re: Which of the following equations has two different roots?  [#permalink]

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18 Nov 2016, 03:27
1
2
in an equation ax^2+bx+c ,if b^2-4ac > 0 then then it has two different solutions
It is only true for choice D, (-5)^2-5(4)=5
Hence D.
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Re: Which of the following equations has two different roots?  [#permalink]

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18 Nov 2016, 08:50
1
1
Bunuel wrote:
Which of the following equations has two different roots?

A. x^2−x+4=0
B. x^2−4x+4=0
C. x^2−3x+9=0
D. x^2−5x+5=0
E. x^2+3x+10=0

Use the property of Quadratic equations -

b^2 −4ac > 0 There are two real roots.

(A) 1 - 16 = - 15 < 0
(B) 16 - 16 = 0
(C) 9 - 36 = - 25 < 0

(D) 25 - 20 = 5 > 0
(E) 9 - 40 = -31 < 0

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Re: Which of the following equations has two different roots?  [#permalink]

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29 Nov 2016, 15:36
Bunuel wrote:
Which of the following equations has two different roots?

A. x^2−x+4=0
B. x^2−4x+4=0
C. x^2−3x+9=0
D. x^2−5x+5=0
E. x^2+3x+10=0

If a quadratic equation in the form of ax^2 + bx + c = 0 has two distinct real roots, then its discriminant b^2 - 4ac > 0. So, let’s check which answer choice has this property.

A. x^2−x+4=0

b^2 - 4ac = (-1)^2 - 4(1)(4) = 1 - 16 = -15, which is NOT greater than 0.

B. x^2−4x+4=0

b^2 - 4ac = (-4)^2 - 4(1)(4) = 16 - 16 = 0, which is NOT greater than 0.

C. x^2−3x+9=0

b^2 - 4ac = (-3)^2 - 4(1)(9) = 9 - 36 = -27, which is NOT greater than 0.

D. x^2−5x+5=0

b^2 - 4ac = (-5)^2 - 4(1)(5) = 25 - 20 = 5, which IS greater than 0.

E. x^2+3x+10=0

b^2 - 4ac = (3)^2 - 4(1)(10) = 9 - 40 = -31, which is NOT greater than 0.

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Re: Which of the following equations has two different roots?  [#permalink]

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22 May 2018, 10:02
Vinayak Shenoy wrote:
Bunuel wrote:
Which of the following equations has two different roots?

A. x^2−x+4=0
B. x^2−4x+4=0
C. x^2−3x+9=0
D. x^2−5x+5=0
E. x^2+3x+10=0

Use the formula to find roots of the equation [-b +/- (sqrt b^2 - 4ac)]/2a
Calculating using the formula gives

A. x^2−x+4=0 imaginary roots b^2 < 4ac
B. x^2−4x+4=0 x= 2, 2 we are asked to find two different roots
C. x^2−3x+9=0 imaginary roots b^2 < 4ac
D. x^2−5x+5=0 two unique roots (5+ sqrt5) , (5- sqrt 5)
E. x^2+3x+10=0 imaginary roots b^2 < 4ac

Hence D

Bunuel how to write the formulas here.
Could you please write my formula correctly? I'm yet to get a hang of this.

When I checked with the instructors from Veritas and Manhattan prep, they told me that GMAT does not test you on imaginary numbers. Kindly clarify as root of negative numbers are imaginary.
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Re: Which of the following equations has two different roots? &nbs [#permalink] 22 May 2018, 10:02
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