Question

if the root of the quadratic equation k²-13x+6=0 are in the ratio 4 :9. find the value of k​

Answer 1

Answer:

let the roots of the equation are 4y and 9y

4y+9y=13/6

13y=13/k

y=1/k

36y2=6/k

36y2=6*y

y=1/6

k=6

Answer 2

Answer:

Let the roots of the equation be 4 and 9 .

One of the root (P)= 4x

Another root (P)= 9x

K²-13x+6=0

P(4) =>k²-13×4+6=0

P(4) =>k²-52+6=0 -----eqn. ( I )

Again,

K²-13x+6=0

P(9)=>K²-13×9+6=0

P(9)=>K²-117+6=0

P(9)=>K²-111=0 -----eqn. (ii)

From eqn.(i) and (ii),We get ,

K²-52+6 = K²-117+6

K²=25

K=√25

K=5.

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