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

Step-by-step solution

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