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The number of ordered pair (a,b) from The set A={1,2,3,4,5} so that The function
F (x) = x3 /3+ ax2 /2+bx+10 is an injective mapping for all x belong to R

Manav Patel , 6 Years ago
Grade 12
anser 2 Answers
Sagar borana

Last Activity: 6 Years ago

If the function is one- one then it should be strictly increaiincor decreasing so f'(x)= x^2+ax+b should have D
Mridul Rabha

Last Activity: 4 Years ago

Given
      f(x)=x³/3+ax²/2+bx+10
     f'(x)=3x²/3+2ax/2+b
     f'(x)=x²+ax+b 
 Since, D
    We know that,
          D=b²-4ac
There fore, 
      D=a²-4b
    a=1,. b=(1,2,3,4,5) = 5 Pairs 
    a=2, b=(1,2,3,4,5) = 5 Pairs
    a=3, b=(3,4,5).      =3 pairs. (remaining doesn't satisfied the                                                                       equ1)
    a=4, b=(4,5).         =2 pairs
    a=5, b=(5).            =0 pairs
Hence, 
             No. Of ordered pair is 15. For injective function.
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