If (2x+ 1) is a factor of the polynomial (8x 3 +bx 2 5x+ 8), then what is the value ofb?
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In factor theorm if (x-a) is the factor of p(x) then p (a)would be the remainder which would be equal to 0.
Zero of the polynomial (2x+1)=0
2x=-1
x=-1/2
p (-1/2)=[8 (-1/2)(-1/2)(-1/2)]+[b (-1/2)(-1/2)]+[5 (-1/2)]+8
=[8 (-1/8)]+1/4b-5/2+8
=-1+1/4b-5/2+8
=9/2 + 1/4b
we know that p (x) = 9/2 + 1/4b which is the factor of (x-a) therefore
9/2 + 1/4b =0
1/4b=-9/2
b=-9/2 × 4
Ans) b=-18
Zero of the polynomial (2x+1)=0
2x=-1
x=-1/2
p (-1/2)=[8 (-1/2)(-1/2)(-1/2)]+[b (-1/2)(-1/2)]+[5 (-1/2)]+8
=[8 (-1/8)]+1/4b-5/2+8
=-1+1/4b-5/2+8
=9/2 + 1/4b
we know that p (x) = 9/2 + 1/4b which is the factor of (x-a) therefore
9/2 + 1/4b =0
1/4b=-9/2
b=-9/2 × 4
Ans) b=-18
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