Question

If sum of the roots of an equation is 5 and sum of cube of roots is 35
The find the equation

Answer 1

Let the roots be x and y for typing privileges!!!
$x + y = 5 \\ {x}^{3} + {y}^{3} = 35$
For objective questions, you can straight away think of such numbers to be 2 and 3, which give you the equation
${a}^{2} - 5a + 6 = 0$
However , for subjective purposes, this won't work. Now I'll be using some shortcuts while typing this so bear with me!!
${(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ 125 = 35 + 3xy(5) \\ xy = 6$
Now we know that a quadratic equation is of the form
${a}^{2} - sa + p$
Where s is the sum of roots and P is the product of roots. Now substituting the values, we get the equation
${a}^{2} - 5a + 6 = 0$