Question

If the difference of quadratic equation is 4 and the difference of their cubes is 208. find the quadratic equation​

Answer 1

Answer:

Let the roots of the equation be a and b

then, a

3

−b

3

=208

and a−b=4

cubing both sides:

(a−b)

3

=64

a

3

−b

3

−3ab(a−b)=64

208−3ab(4)=64

144=12ab

ab=12

Similarly, (a+b)

2

=(a−b)

2

+4ab

(a+b)

2

=4

2

+4(12)

(a+b)

2

=16+48

a+b=±8

The general form of equation is x

2

−Sx+P=0, hence the equation will be

x

2

±8x+12=0