1.

In polynomial p(x) = ax3 + bx2 + cx + d, p(l) = p(-l). Prove that a + c = 0.

Answer»

p(x) = ax3 + bx2 + cx + d

p(l) = a(1)3 + b(1)2 + c(1) + d

= a + b + c + d

p(-1) = a(-1)3 + b(-1)2 + c(-1) + d

= -a + b – c + d

p(1) = p(-1) is given ie, a + b + c + d = -a + b – c + d

2a + 2c = 0; 2(a + c ) = 0;

ie, a + c = 0


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