Quadratic Polynomial
Level
pending
Let f(x) is a quadratic polynomial such that f(x) >=0 and f(1)=0,f(2)=8. Find f(3)
The answer is 32.
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1 solution
Let equation be ax^2 +bx + c. F(1) = o, so a + b + c =0. And f(2)=8, so 4a +2b+c=0. Now f(x) minimum occurs at -b/2a. 1 is a zero of the polynomial..and its also its minimum value( given). So both its roots coincide..so B^2 = 4ac Since its minimum value( which is 0) occurs at 1, -b/2a= 1 Solving for a, b , c..we get this equation- 8x^2 -16x + 8.. Putting x = 3.. we get f(3)= 32