f(x+h)=0 represents the transformed equation of the equation f(x)=x^4+2 x^3-19 x^2-8 x+60=0 . If this transformation removes the term containing x^3 from f(x)=0 , then h=

Step-by-step solution

Given, f(x)=x^4+2 x^3-19 x^2-8 x+60=0 Now, f(x+h)=0 aligned & (x+h)^4+2(x+h)^3-19(x+h)^2-8(x+h)+60=0 & x^4+4 x^3 h+6 x^2 h^2+4 x h^3+h^4+2 x^3+2 h^3 aligned aligned & +6 x h(x+h)-19(x+h)^2-8(x+h)+60 aligned =0 It does not contain x^3 So, 4 h+2=0 h= -2 4 = -1 2