p(x) = 2x3 + ax2 – 7x + b
We have p(1) = 3.
p(1) = 2 x 13 + a x 12 – 7 x 1 + b = 3
2 + a – 7 + b = 3
a + b – 5 = 3
a + b = 8 ………. (1)
We have p(2) = 19.
p(2 ) = 2 x 23 + a x 22 – 7 x 2 + b = 19
16 + 4a – 14 + b = 19
4a + b + 2 = 19
4a + b = 17…….. (2)
From equation (1), (2)
(2) – (1) 4a + b = 17
\(\frac{a+b=8}{3a=9}\)
a = 9/3 = 3
From equation (1)
a + b = 8
3 + b = 8
b = 5