Question

If x=3 is one roots of the quadratic equation (x)2-2k-6=0 then find value k

Answer 1

Hey... I think this can be ur answer!!

Polynomial - x2 - 2kx - 6 =0
P (3)=(3)2 - 2(3)k =6
=9 - 6k =6
=-6k =-3
=k =1/2

Hope it helps you dear ☺️☺️

Answer 2

Mistake in your question.

Question:

If x = 3 is one roots of the quadratic equation $x^2-2kx-6=0$ then find value k.

Answer:

The value of k is $\frac{1}{2}$.

Solution:

Given quadratic equation is $x^2-2kx-6=0$.

(x – 3) is one root of the given quadratic equation.

Factor theorem:

A polynomial f(x) has a root (x – a), then f(a) = 0.

By factor theorem,

x – 3 = 0

x = 3

Substitute x = 3 in quadratic equation.

$3^2-2k(3)-6=0$

$9-6k=6$

Subtract 9 from both sides of the equation.

$-6k=-3$

Divide by –6 on both sides of the equation.

$k=\frac{1}{2}$

The value of k is $\frac{1}{2}$.

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