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Let f(x)=x^2+4 x+a and g(x)=x^2+6 x+2 a be two functions and another function h(x)= f(x) g(x) g(x) 0 . Then find the sum of all integral values of a for which y=h(x) is an onto function.

Correct answer

6

Step-by-step solution

h(x)= x^2+4 x+a x^2+6 x+2 a is an onto function means range ' R '. ^2+6 +2 a=0 ^2+4 +a=0 2 =-a = -a 2 a^2 4 -4 ( a 2 )+a < 0 a(a-4) < 0 a (0,4) a=1+2+3=6

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