# If One Root of the Quadratic Equation Kx2 – 7x + 12 = 0 is 3, Then Find the Value of K - Algebra

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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