Question

If the difference of roots of quadratic equation is 4 and difference of their cube is 208.Find quadratic equation.
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Answer 1

Answer:

b² + 4b - 12 = 0

Step-by-step explanation:

Let the no. be a & b.

now a - b = 4

a = 4 + b

and a³ - b³ = 208

(a-b)(a² + ab + b²) = 208

4(a² + ab + b²) = 208

now put the value of a from the above equation.

(4+b)² + b(4+b) + b² = 52

16 + b² + 8b + 4b + b² = 52

3b² + 12b - 36 = 0

b² + 4b - 12 = 0