Question

if alpha and beta are the zeroes of x^2-x+k and 3 alpha+2 beta =20 then find the value of k​

Answer 1

Answer:

Given that α and β are the roots of the polynomial f(x)=x  

2

−x−k

such that α−β=9

To find k,

Squaring on both sides of the equation α−β=9,gives,

α  

2

+β  

2

−2αβ=81

⟹(α+β)  

2

−4αβ=81

⟹1+4k=81

⟹4k=80

⟹k=20

The sum and product of the roots are determined from the given polynomial.

Step-by-step explanation:

Answer 2

Answer:

-306

Step-by-step explanation:

x^2-x+k=0

α+β=-(-1)=1

αβ=k

3α+2β=20

α+β=1 -multiply with 3

3α+3β=3

now

3α+2β=20

3α+3β=3

(-) (-) (-)

________

0-β=17

β=-17

α+β=1

α+(-17)=1

α=1+17

α=18

now αβ=k

-17×18=k

-306=k