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The polynomial P(x) = ax^2 + bx + 4 is divisible by x - 2 and x - 1. What are a and b

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xataexa | Student, Kindergarten | Salutatorian

Posted September 23, 2013 at 5:20 AM via web

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The polynomial P(x) = ax^2 + bx + 4 is divisible by x - 2 and x - 1. What are a and b

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 23, 2013 at 5:24 AM (Answer #1)

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If a polynomial P(x) is divisible by x - a, P(a) = 0.

The polynomial P(x) = ax^2 + bx + 4 is divisible by x - 2 and x - 1.

This gives: P(2) = 0 and P(1) = 0

P(2) = 0

=> a*4 + b*2 + 4 = 0

P(1) = 0

=> a + b + 4 = 0

a + b + 4 = 0

=> a = -4 - b

Substitute in a*4 + b*2 + 4 = 0

=> (-4 - b)*4 + 2b + 4 = 0

=> -16 - 4b + 2b + 4 = 0

=> -2b = 12

=> b = -6

a = 2

The value of a = 2 and b = -6; the polynomial P(x) = 2x^2 - 6x + 4

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aruv | High School Teacher | Valedictorian

Posted September 23, 2013 at 8:46 AM (Answer #2)

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`p(x)=ax^2+bx+4`  ,P(x) is divisible by x-1 and x-2.

Thus

P(1)=0 and P(2)=0

Therefore

`a+b+4=0`      (i)

`4a+2b+4=0`

`2a+b+2=0`    (ii)

Subtract (ii0 from (i) ,we have

-a+2=0

a=2

substitute a=2 in (i)

2+b+4=0

b=-6

Thus a=2 and b=-6 .

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