Question

difference of roots of the quadratic equation is 3 and difference of their cubes is 200 find the quadratic equation​

Answer 1

Answer:

solved

Step-by-step explanation:

roots be m , n

m³ - n³ = 200 = (m-n)(m²+n²+mn)

m - n = 3

m²+n²+mn = 200/3 , m = n+3

(n+3)² + n² + n(n+3) = 200/3

3n²+9n - 173/3 = 0

  n²+3n - 173/9 = 0

n = -3±√773/3 ÷2 = -3/2 ± √773/6

m =  3/2 ± √773/6

m+n = ±√773/6

mn = 773/36 - 9/4 = 178/9

since there are two values of m and  two values of n

we shall have  two values of quadratic equations ;

x² ±√773/6 + 178/9 = 0