If alpha , beta are zeroes of x^(2) - x - 6 then find the value of (1). alpha ^3 + beta ^(3) (2). alpha- beta
Answers
Answer:
1) 19
2) 5 or -5
Step-by-step explanation:
Roots of quadratic equations are, α and β
Quadratic equation :-
→ x²-x-6
To Find :-
α³-β³=(α+β)(α²+β²-αβ)
=(α+β)[(α+β)²-3αβ]
Sum of roots. α+β= -b/a
Product of roots = c/a
Here, sum of roots = 1
product of roots= -6
So,
a) (1)[(1)²-3(-6){
=> 1[1+18]
=> 19
Now,
b) α-β = ?
lets take out the roots,
x²-x-6
=> x²-3x+2x-6
=> x(x-3)+2(x-3)
=> (x+2)(x-3)=0
roots are, x= -2 and 3
Therefore,
α-β = -2-3= -5
or
α-β= 3-(-2)
=> α-β= 3+2=5
So,
α³-β³= 19 and α-β= 5 or -5
Ans.
Answer:
Answer:
1) 19
2) 5 or -5
Step-by-step explanation:
Roots of quadratic equations are, α and β
Quadratic equation :-
→ x²-x-6
To Find :-
α³-β³=(α+β)(α²+β²-αβ)
=(α+β)[(α+β)²-3αβ]
Sum of roots. α+β= -b/a
Product of roots = c/a
Here, sum of roots = 1
product of roots= -6
So,
a) (1)[(1)²-3(-6){
=> 1[1+18]
=> 19
Now,
b) α-β = ?
lets take out the roots,
x²-x-6
=> x²-3x+2x-6
=> x(x-3)+2(x-3)
=> (x+2)(x-3)=0
roots are, x= -2 and 3
Therefore,
α-β = -2-3= -5
or
α-β= 3-(-2)
=> α-β= 3+2=5
So,
α³-β³= 19 and α-β= 5 or -5
Step-by-step explanation:
Hope this answer will help you.