Question

If one root of the quadratic equation kx² – 7x + 12 = 0 is 3, then find the value of k.

Answer 1

The given quadratic equation is kx² - 7x + 12 = 0.
Let α and β be the roots of the given equation.
Comparing the given equation with the standard equation,
ax²+ bx+ c =0, we have,
a = k, b =- 7 and c 12.

`Thus ,alpha+beta=-b/a=-(-7)/k`

`and alphabeta=c/a=12/k`

Since one of the roots is 3, we have,

`3+beta=7/k and 3beta=12/k`

`3+beta=7/k and beta=4/k`

Substituting the value of `beta=4/k `

`3+4/k=7/k`

`(3k+4)/k=7/k`

`3k+4=7`

`3k=7-4`

3k=3

k=1