Question

If p(m) = m3+ 2m2- m+ 10 then p,(a) + p(- a) = ?​

Answer 1

p(m) = m3 + 2m2 – m + 10

Put m = a in the given polynomial.

∴ p(a) = a3 + 2a2 – a + 10 …(i)

Put m = -a in the given polynomial.

p(-a) = (-a)3 + 2(-a)2 – (-a) +10

∴ p(-a) = -a3 + 2a2 + a + 10 …(ii)

Adding (i) and (ii),

p(a) + p(-a) = (a3 + 2a2 – a + 10) + (-a3 + 2a2 + a + 10)

= a3 – a3 + 2a2 + 2a2 – a + a + 10 + 10

∴ p(a) + p(-a) = 4a2 + 20