Question

If α and β are the roots of the polynomial x2

-5x+k and α-β =1, then find the

value of k​

Answer 1

Answer:

k = 6

Step-by-step explanation:

GIVEN:

x^2 - 5x + k

a = 1 [coefficient of x^2]

b = -5 [ coefficient of x]

c = k [constant]

α - β = 1 --------(i)

α + β = -b/a

        = -(-5)/1

α + β  = 5-----------(ii)

αβ = c/a = k/1

αβ = k -----------(iii)

By elimination method,

(i) ------ α + β = 5

(ii)------  α - β = 1

          --------------

           2α    = 6

α = 6/2

α = 3

Substituting α = 3 in (i)

α + β = 5

3 + β = 5

β = 5 - 3

β = 2

Substituting α = 3 and β = 2 in (iii)

αβ = k

3 x 2 = k

k = 6