Question

In the polynomial ax³+bx²+cx+d.If p(2)=p(-2).prove that 4a+c=0
find ??​

Answer 1

$p(x) = a {x}^{3} + b {x}^{2} + cx + d \\then \\ p(2) = a( {2}^{3} ) + b(2 {}^{2} ) + c(2) + d \\ = 8a + 4b + 2c + d \\ p( - 2) = a( { - 2}^{3} ) + b( { - 2}^{2} ) + c( - 2) + d \\ = - 8a + 4b - 2c + d$

$given \: that \: \\ p(2) = p( - 2) \\ 8 a + 4b + 2c + d = - 8a + 4b - 2c + d \\ 8a + 2c = - 8a - 2c \\ 8a + 8a + 2c + 2c = 0 \\ 16a + 4c = 0 \\ 4(4a + c) = 0 \\ 4a + c = 0 \\ hence \: proved$