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Q. if f(x) is a quadratic expression suc...

Q. if f(x) is a quadratic expression such that f(x)>0 AA x epsilon R, and if g(x)=f(x)+f'(x)+f(x), then prove that g(x)>0 x epsilon R. Let f(x)=ax^2+bx+c Given that f(x)>0 so >0, b^2-4ac<0 Now g(x)=ax^2+bx+c+2ax+b+2a=ax^2+(b+2a)x+(b+c+2a) for this quadratic expression a>0 and discriminant

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