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01 Apr 2020, 21:47
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E
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Difficulty:
25%
(medium)
Question Stats:
74% (01:43) correct
26%
(01:36)
wrong
based on 289
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If y = x^2+bx+c which has two real roots, Find the value of b+c?
1) Sum of the roots of given equation is 5
2) both the roots of given equation are integers
1) Sum of the roots of given equation is 5
2) both the roots of given equation are integers
Source: www.GMATinsight.com
01 Apr 2020, 23:13
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y = x^2+bx+c which has two real roots, so, b^2-4c ≥0
ST (1) : Sum of the roots of given equation is 5
So, -b /1 = 5
or, b= -5
also, 25-4c ≥0
or, c ≤ 6.25
so, b+c does not have any unique value. insufficient
[example : x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 ]
ST(2) : both roots are integers .
so b and c are multiples of a (here a=1) and b^-4c is a multiple of a^2 (a=1)
but we don't find unique value of b+c . insufficient
[example : x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 ]
combining both , we can take similar examples x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 but cant find unique value of a+b. so insufficient
answer will be E imo.
ST (1) : Sum of the roots of given equation is 5
So, -b /1 = 5
or, b= -5
also, 25-4c ≥0
or, c ≤ 6.25
so, b+c does not have any unique value. insufficient
[example : x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 ]
ST(2) : both roots are integers .
so b and c are multiples of a (here a=1) and b^-4c is a multiple of a^2 (a=1)
but we don't find unique value of b+c . insufficient
[example : x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 ]
combining both , we can take similar examples x^2-5x +4 =0 ; b+c = -1 but x^2 - 5x +6 =0 ; b+c = 1 but cant find unique value of a+b. so insufficient
answer will be E imo.
