Find the value of p, if (2x-1) is a factor of 2x^(3)+px^(2)+11x+p+3
Share
Find the value of p, if (2x-1) is a factor of 2x^(3)+px^(2)+11x+p+3
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
(2X-1) is a factor of the given Polynomial.
(2X -1) = 0
2X = 1
X = 1/2
P(X) = 2X³ + PX² + 11X + P + 3
P(1/2) = 0 because 1/2 is a zero of the given Polynomial.
P(1/2) = 0
2 × (1/2)³ + P × (1/2)² + 11 × 1/2 + P + 3 = 0
2 × 1/8 + P × 1/4 + 11/2 + P + 3 = 0
1/4 + P/4 + 11/2 + P + 3 = 0
1 + P + 22 + 4P + 12 / 4 = 0
4P + P + 1 + 22 + 12 = 0 × 4
5P + 35 = 0
5P = -35
P = -35/5
P = -7.
HOPE IT WILL HELP YOU....... :-)
So, 2x - 1 = 0
x = 1/2
×××××××××××××××××××
Putting the value of x in given equation,
2x³ + px² + 11x + p + 3 = 0
2(1/2)³ + p(1/2)² + 11(1/2) + p + 3 = 0
2(1/8) + p(1/4) + 11/2 + p + 3 = 0
1/4 + p/4 + 11/2 + p + 3 = 0
p + p/4 = -3 - 1/4 - 11/2
(4p + p)/4 = (-12 - 1 -22)/4
5p = -35
p = -35/5
p = -7
I hope this will help you
(-: