Find the value of p, if (2x-1) is a factor of 2x3+px2+11x+p+3
Answers
Answered by
35
F(x) = 2x^3 +px^2 + 11x + p + 3
=> F(1/2) = 0
=> (2) (1/2)^3 + p(1/2)^2 + 11(1/2) + p + 3 = 0
=> 1/4 + p/4 + 11/2 + p + 3 = 0
=> (1+ p + 22 + 4p + 12) /4 = 0
=> 5p + 35 = 0
=> 5p = - 35
=> p = - 7
=> F(1/2) = 0
=> (2) (1/2)^3 + p(1/2)^2 + 11(1/2) + p + 3 = 0
=> 1/4 + p/4 + 11/2 + p + 3 = 0
=> (1+ p + 22 + 4p + 12) /4 = 0
=> 5p + 35 = 0
=> 5p = - 35
=> p = - 7
Answered by
7
Step-by-step explanation:
2x - 1 = 0
x = 1/2
2 (1/2)3 + p (1/2)2 + 11 (1/2) + p + 3
= 2×1/8 + p × 1/4 + 11 × 1/2 + p + 3
= 1/4 + p/4 + 11/2 + p + 3
= ( 1 + p + 22 + 4p + 12 )/4 = 0
= 5p + 35 = 0
= 5p = -35
= p = -35/5
= p = -7
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