Quadratics

consider p(x) = ax²+bx+c

since p(x) ≥ 0

graph of quadratic shud be some wat like wat i hav shown

it will hav only one x for wich p(x) = 0 wich is 1

since p(1) = 0

thus b²-4ac = 0

and thus 1 = -b/2a

thus b + 2a = 0 .....(1)

p(2) = 2

i.e

4a+ 2b + c = 2 (2a+b ) + c = 2

thus c = 2 .......(2)

now p(1) = 0

a+b+c = 0 ..(3)

frm (1), (2), (3)

- a + c = 0

a =c = 2

and thus b = -2a = -4

thus p(0) + p(3)

= c + 9a + 3b + c

= 2 c +9a+3b

= 2(2) + 9(2) + 3 ( -4 )

= 4 + 18 - 12

= 10