Q.If A = {x/6x²+x-15 = 0}, B = {x/2x²-5x-3 = 0}, C = {x/2x²-x-3 = 0} then find (A∪B∪C).

Solve each quadratic. For A: $6x^2+x-15=0$, discriminant $= 1+360=361=19^2$, so $x=\frac{-1\pm19}{12}$, giving $x=\frac{18}{12}=\frac{3}{2}$ or $x=\frac{-20}{12}=-\frac{5}{3}$. So $A=\left\{\frac{3}{2}, -\frac{5}{3}\right\}$. For B: $2x^2-5x-3=0$ factors as $(2x+1)(x-3)=0$, giving $x=-\frac{1}{2}$ or $x=3$. So $B=\left\{-\frac{1}{2}, 3\right\}$. For C: $2x^2-x-3=0$ factors as $(2x-3)(x+1)=0$, giving $x=\frac{3}{2}$ or $x=-1$. So $C=\left\{\frac{3}{2}, -1\right\}$. Taking the union of all elements that …

Solve each quadratic equation for its roots (factor or use the quadratic formula), then collect every distinc …

Since $\frac{3}{2}$ is a common root of A and C, it must be listed only once in the union — do not repeat i …