4Thanks QWERTY
The quadratic polynomial has the following properties : p(x) ≥ 0 for all real no.s , p(!) = 0 & p(2) = 2.Find the value of p(0) + p(3)
Ans : 10
(I wan't solution)
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UP 0 DOWN 0 0 2
2 Answers
23
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