Question

if one root of the equation 2x^2-12x+k =0 be twice the other, find the value of k.

Answer 1

Heya !!!



Let alpha be the one root of the given polynomial.



Other root will be 2Alpha .




P(X) = 2X² - 12X + K



Here,


A = 2 , B = -12 and C = K






Sum of zeros = -B/A





Alpha + 2Alpha = 12/2





3Alpha = 6




Alpha = 6/3 = 2




And,




Product of zeroes = C/A




Alpha + 2Alpha = K/2





3Alpha = K/2




3 × 2 = K/2






K = 6 × 2




K = 12




★ HOPE IT WILL HELP YOU ★

Answer 2

Answer:

Answer:

So using Vietas Formula(root1+root2=opposite of linear term)

we know that:

root1+root2=12

and

root1=2(root2)

if we plug this equation in with the first one we get:

2(root2)+root2=12

3(root2)=12

root2=4

if root2 is 4 then:

root1+4=12

and root1=8

and now also using Vietas formula,  we know that (root1)(root2)=k

so :

(8)(4)=k

k=32

Step-by-step explanation: