if a, b are the roots of equation x²-px+q=0 , find the equation with roots a² +b and a+b²
Answers
Answered by
1
Step-by-step explanation:
a, b are roots of x²-px+q = 0
a+b = -(-p)/ 1=p
ab = q/1 = q
a²+b,a+b² are roots
sum of roots = a²+a+b+b²
add and subtract 2ab
= a²+b²+2ab -2ab +a+b
= (a+b)²-2ab+a+b
= p²-2q+p
product of roots = (a²+b)(a+b²) = a³+a²b²+ab+b³
= a³+b³+(ab)²+ab
= (a+b)(a²+b²-ab)+ (ab)² + ab
=(a+b)((a+b)²-3ab)) + (ab)² +ab
= p(p²-3q) + q² + q
= p³-3pq +q²+q
equation is x²-(sum of roots)x + product of roots
= x²-(p²-2q+p)x + p³-3pq+q²+q
Similar questions