NDA2022MathematicsQuadratic EquationActual
Let and be the roots of the equation x^2+p x+q=0 . If ^3 and ^3 are the roots of the equation x^2+m x+n=0 , then what is the value of m+n ?
Options
- Ap^3+q^3+p q
- Bp^3+q^3-p q
- Cp^3+q^3+3 p q
- Dp^3+q^3-3 p q
Correct answer
D. p^3+q^3-3 p q
Step-by-step solution
Given that , are roots of equation x^2+p x+q=0 + =-p and . =q and ^3 and ^3 are roots of equation x^2+m n+n=0 ^3+ ^3=( + )^3-3 ( + )=-m -p^3+3 p q=-m m=p^3-3 p q ^3 ^3=( )^3=q^3=n m+n=p^3+q^3-3 pq [ from (i) and (i i)]