Question

If alpha , beta are zeroes of x^(2) - x - 6 then find the value of (1). alpha ^3 + beta ^(3) (2). alpha- beta​

Answer 1

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 2

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.