If A + B = 1 and (x — 2) is a factor of x2 + Ax + B, find the value of B

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11 Oct 2010 Find the value of B

If A + B = 1 and (x — 2) is a factor of x2 + Ax + B, find the value of B

OPtion

1) 1
2) 4
3) 3
4) 5
5) -5
6) -4
7) 6
8) -6
9) 8
10) 7

Solution

(x - 2) is a factor of x^2 +Ax + B
so 4 + 2A + B = 0
=> 2A + B = -4
also A+B=1
Solving to get A = -5
B = 6

Correct Option: 7 Best Solution (12)

Dr.Dipin Singh   13 years AGO

If A + B = 1 and (x — 2) and (x-y)are factors of x2 + Ax + B, then A = - (2+y) and B= 2y; then A+B= 2y -2-y = 1 ( given ) or y=3; Hence B=2*3=6

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S. Singh   13 years AGO

A= -5, B=6, x2 + Ax + B= x2 -5x + 6

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Dimple   13 years AGO

If f is other root of x2 + Ax + B, then
x2 + Ax + B = (x-2)(x-f) = x^2- (2+f)x+2f', so A= -(2+f) and B= 2f and A+B=1. solving these we get B=6and eqn becomes x^2 -5x + 6 .

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Bawa   13 years AGO

A = - sum of roots and B= product of roots. using this property , we get A=-5 and B=6 for roots 2 and 3 for eqn x^2+Ax+B =0.

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Jason   13 years AGO

If A + B = 1 and (x — 2) is a factor of x2 + Ax + B, the value of B is 6 and Value of A is -5.

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Sulekha   13 years AGO

A=-5 and B=6 will satisfy given conditions.

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SUDESHNA SEN   13 years AGO

x-2 is a factor of the equation.
So, x-2=0 or x=2.Putting x=2 in x^2+Ax+B=0, we have, 4+2A+B=0,
or, 2A+B=-4.... (1)
and A+B=1..... (2)
Solving (1) and (2), we have A=-5 and B= 6..... Option 7)

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JAYEETA DESHMUKH   13 years AGO

x-2 is a factor of the equation.
So, x-2=0 or x=2.Putting x=2 in x^2+Ax+B=0, we have, 4+2A+B=0,
or, 2A+B=-4.... (1)
and A+B=1..... (2)
Solving (1) and (2), we have A=-5 and B= 6..... Option 7)

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Tridib Das   13 years AGO

Let the other factor of (x2 + Ax + B) be (x - y)
Therefore, (x-2)(x-y)= x2 + Ax + B,
or, x2 + x(-2-y) + 2y = x2 + Ax + B,
or, (-2-y)x + 2y = Ax + B,
or, A = (-2-y) & B = 2y,
Again, A + B = 1, or, A = 1 - B,

Therefore, (1-B) = (-2-y), or, B = 3+y
So, 3+y = 2y, or, y = 3.

Therefore, B = 3+y = 3+3 = 6.

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Chetan Vinayak Vidhate   13 years AGO

another factor is (x-3) which makes eq

x2-5x+6

Ans:
A= -5
B= 6

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YadeeshKumar   13 years AGO

gn A+B=1
x-2 is a factor of x2+Ax+B
therefore
x2+Ax+B=0 substitute x as 2
4+2A+B=0 substitute A=1-B
4+2(1-B)+B=0
4+2-2B+B=0
6-B=0
B=6

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Md Intshamuddin   13 years AGO

Let x2+Ax+B=(x-2)(x-C),or,x2+Ax+B=x2-(C+2)x+2C,or,Ax+B=-(C+2)x+2C,seperating the coeff. of x& const. we get,A=-(C+2),B=2C,now,A+B=-(C+2)+2C,or,1=C-2,or,C=3,hence B=2C=2*3=6

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