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If y = x^2+bx+c which has two real roots, Find the value of b+c? 1) S  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 67% (01:35) correct 33% (01:41) wrong based on 33 sessions

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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

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Re: If y = x^2+bx+c which has two real roots, Find the value of b+c? 1) S  [#permalink]

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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 Re: If y = x^2+bx+c which has two real roots, Find the value of b+c? 1) S   [#permalink] 01 Apr 2020, 22:13

# If y = x^2+bx+c which has two real roots, Find the value of b+c? 1) S  