If f(x)= array cl x^2-1, & 0 < x < 2 2 x+3, & 2 x < 3 array . ,the quadratic equation whose roots are _ x 2⁻ f(x) and _ x 2⁺ f(x) is

Step-by-step solution

f(x)= cases x^2-1, & 0 < x < 2 2 x+3, & 2 x < 3 cases Now, _ x 2⁻ f(x)= _ x 2⁻ x^2-1= _ h 0 [(2-h)^2-1 ]= _ h 0 [4+h^2-4 h-1 ]=4+0-0-1=3 and _ x 2⁺ f(x)= _ x 2⁺ (2 x+3)= _ h 0 2(2+h)+3= _ h 0 4+2 h+3=4+0+3=7 Therefore, the quadratic equation whose roots are 3 and 7 is given by x^2-(3+7) x+(3 7)=0 which is x^2-10 x+21=0