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08 Jun 2020, 12:25
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E
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Difficulty:
65%
(hard)
Question Stats:
61% (02:24) correct
39%
(01:58)
wrong
based on 225
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Not Attempted Yet
I. x^2 - 6x + 55 = 0
II. 2x^2 - 4x - 70 = 0
III. x(x + 7) = 44
Given the three quadratic equations above, which pair of equations has at least one common root?
A. I and II
B. II and III
C. I and III
D. I, II and III
E. None of the above
II. 2x^2 - 4x - 70 = 0
III. x(x + 7) = 44
Given the three quadratic equations above, which pair of equations has at least one common root?
A. I and II
B. II and III
C. I and III
D. I, II and III
E. None of the above
08 Jun 2020, 12:40
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Equation 1 :- No possible solution as D i.e. b^2-4ac is less than zero; or Quadratic equation graph will be always above x (a>0) and will not cut x ;
Equation 2 :- x=(-)5 and 7
Equation 3 :- x= 4 and (-) 11
So no two-equation have same roots
Equation 2 :- x=(-)5 and 7
Equation 3 :- x= 4 and (-) 11
So no two-equation have same roots
yashikaaggarwal
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08 Jun 2020, 12:52
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Discriminant of Equation
I. x^2 - 6x + 55 = 0
=> D = b^2-4ac
=> D = 36-220
=> D = -184 (No real roots)
Discriminant of Equation
II. 2x^2 - 4x - 70 = 0
=> D = b^2-4ac
=> D = 16-4*-(70)*2
=> D = 16+560 = 576 (real roots) => √D = 24
Roots = -b±√D/2a
=> 4+24/2*2 = 28/4 => 7
=> 4-24/2*2 = -20/4 => -5
Discriminant of Equation
III. x(x + 7) = 44
=> D = b^2-4ac
=> D = 49-4*-(44)*1
=> D = 49+176 = 225 (real roots) => √D = 15
Roots = -b±√D/2a
=> -7+15/2*1 = 8/2 => 4
=> -7-15/2*1 = -22/2 => -11
None of the equation share same roots.
Answer is supposedly E
Posted from my mobile device
I. x^2 - 6x + 55 = 0
=> D = b^2-4ac
=> D = 36-220
=> D = -184 (No real roots)
Discriminant of Equation
II. 2x^2 - 4x - 70 = 0
=> D = b^2-4ac
=> D = 16-4*-(70)*2
=> D = 16+560 = 576 (real roots) => √D = 24
Roots = -b±√D/2a
=> 4+24/2*2 = 28/4 => 7
=> 4-24/2*2 = -20/4 => -5
Discriminant of Equation
III. x(x + 7) = 44
=> D = b^2-4ac
=> D = 49-4*-(44)*1
=> D = 49+176 = 225 (real roots) => √D = 15
Roots = -b±√D/2a
=> -7+15/2*1 = 8/2 => 4
=> -7-15/2*1 = -22/2 => -11
None of the equation share same roots.
Answer is supposedly E
Posted from my mobile device
