Question : If $\alpha, \beta$ are the roots of $6 x^2+13 x+7=0$, then the equation whose roots are $\alpha^2, \beta^2$ is:

Option 1: $36 x^2-87 x+49=0$

Option 2: $36 x^2-85 x+49=0$

Option 3: $36 x^2-85 x-49=0$

Option 4: $36 x^2+87 x-49=0$

Question : If the sum of the roots of a quadratic equation is 1 and the product of the roots is –20, find the quadratic equation.

Option 1: $x^{2}–x–20=0$

Option 2: $x^{2}+x+20=0$

Option 3: $x^{2}+x–20=0$

Option 4: $x^{2}–x+20=0$

Question : If $\alpha$ and $\beta$ are the roots of equation $x^{2}-x+1=0$, then which equation will have roots $\alpha ^{3}$ and $\beta ^{3}?$

Option 1: $x^{2}+2x+1=0$

Option 2: $x^{2}-2x-1=0$

Option 3: $x^{2}+3x-1=0$

Option 4: $x^{2}-3x+1=0$