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