1what is meant by real roots (t/f) ? is it true / false ?
let f(x) be a quadratic polynomial with +ve integral coefficients and such that for every real a,b when b>a a∫b f(x)>0
also g(x)=f''(x)f(x) and g(0)=12
then
a.total no. of quadratic polynomial is_____
b.f(x)=0 has real roots(t/f)
c.max value of f(1)__
d.min value of f(1)__
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6 Answers
66Let f(x)=Ax2 + Bx + C
It is quite obvious that f cannot have real roots and the graph of y = f(x) must open upward. So A ≥ 1. Further, C ≥ 1. Also B2 < 4AC.
g(x)=2A(Ax2 + Bx + C)
g(0)=2AC = 12
giving AC = 6. So, the possibilities are
i) A = 1, C = 6.
ii) A = 2, C = 3
iii) A=3, C = 2
iv) A = 6, C =1
In all these cases, B2 < 24. So B can be 1, 2, 3, 4.
So there are 16 such function f possible.
f(1) = A + B + C. So its maximum possible value is 11 and minimum is 6.