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If 2 and -2 are the zeroes of the polynomial `P(x) = ax^4 +2x^3 -3x^2+ bx -4` , find...

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user2179659 | eNotes Newbie

Posted June 29, 2013 at 6:00 AM via web

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If 2 and -2 are the zeroes of the polynomial `P(x) = ax^4 +2x^3 -3x^2+ bx -4` , find the values of a and b.

 

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llltkl | College Teacher | (Level 3) Valedictorian

Posted June 29, 2013 at 6:31 AM (Answer #1)

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The given polynomial is `P(x) = ax^4 +2x^3 -3x^2+ bx -4`

Since 2 and -2 are the zeroes of the polynomial P(x), therefore, (x-2) and (x+2) are the factors of the equation P(x)=0.

It follows that,

`P(2)=0`

`rArr a*2^4+2*2^3-3*2^2+b*2-4=0`

`rArr 16a+16-12+2b-4=0`

`rArr 16a+2b=0`

`rArr 8a+b=0 ---- (i)`

and

`P(-2)=0`

`rArr a*(-2)^4+2*(-2)^3-3*(-2)^2+b*(-2)-4=0`

`rArr 16a-16-12-2b-4=0`

`rArr 16a-2b-32=0`

`rArr 8a-b=16 ----- (ii)`

adding eq.s (i) & (ii),

`16a = 16`

`rArr a =1`

Putting this value of a in eq. (i),

`8*1+b = 0`

`rArr b=-8`

Hence a =1, b=-8.

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