Question

state whether x is equal to minus K upon 2 is root of quadratic equation 2 X square + bracket K - 6 bracket close x minus 3 is equal to zero

Answer 1

Hope this answer helps you

Answer 2

No,  $x=-\frac{k}{2}$ is not a root of given quadratic equation.

Step-by-step explanation:

The given equation is

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

We need to check whether $x=-\frac{k}{2}$ is a root of given quadratic equation.

If $x=-\frac{k}{2}$ is a root of given quadratic equation, then the given equation is true for

Taking LHS

$LHS=2x^2+(k-6)x-3$

Substitute $x=-\frac{k}{2}$ in the above expression.

$LHS=2(-\dfrac{k}{2})^2+(k-6)(-\dfrac{k}{2})-3$

$LHS=\dfrac{k^2}{2}-\dfrac{k^2}{2}+3k-3$

$LHS=3k-3$

$LHS\neq 0$

$LHS\neq RHS$

The given equation is not true for $x=-\frac{k}{2}$.

Therefore, $x=-\frac{k}{2}$ is not a root of given quadratic equation.

#Learn more

If (-4) is a zero of polynomial x^2-x-(2+k), then find the value of k.

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