Question

Il one zero of the polynomial p(x) = x2 - 6x +k is twice the other the
find the value of k.​

Answer 1

Answer:

8

Step-by-step explanation:

Polynomials written in form of x^2 - Sx + P, represent S as sum of their roots and P as product of their roots.

So, in polynomial p(x) = x^2 - 6x + k, if a is one zero another should be 2a.

= > sum of roots = 6

= > a + 2a = 6

= > 3a = 6

= > a = 2

Product of roots = k

= > 2a * a = k

= > 2a² = k

= > 2(2)² = k

= > 2(4) = k

= > 8 = k

Answer 2

Let α & β be zeros of the polynomial x² - 6x + k.

Let β = 2α

Here, a=1, b=-6 & c=k

α+β = -b/a = 6 ......................(i)

αβ = c/a = k ..........................(ii)

From (i) :–

β = 6-α ..........................(iii)

Putting β = 2α in (iii) :–

2α = 6-α

3α = 6

α = 2

β = 2α

β = 2×2 = 4

k = αβ = 2×4 = 8

k = 8