Question

if the difference of roots of the quadratic equation is 3 and difference of their cubes is 279 find the quadratic equation​

Answer 1

Step-by-step explanation:

let roots are a and b

a-b=3 squaring both Sides (a-b)2=9=a2+b2-2ab=9 a2+b2=9+2ab

also a3-b3=279

(a-b)(a2+ab+b2) =279

now from above put values

3*(9+2ab+ab)=279

9+3ab=93

3ab=93

ab=31

a2+b2+2ab=9ab+2ab+2ab=13ab

(a+b)2=403

a+b=√403

now quadratic equation is as follows

x2-x(a+b)+ab

so our equation becomes

x2-√403x+31