Question

Find the quadratic equation sum of whose roots is 3 and the sum of the cubes of roots is 7

Answer 1

Let the two roots are a and b,

we know the formula that,

(a+b)³ = a³ + b³ + 3ab(a+b)

=> 3³ = 7 + 3ab(3)

=> ab = 20/9

Now we know that a quadratic equation with roots a and b  can be formed as :

x² - x(a+b) + ab = 0

=> x² - 3x + 20/9 = 0

=> 9x² -27x + 20 = 0

which is the required quadratic equation.