# Given #2x^2-kx+(k-2) = 0#, is there some value of #k# such that both roots are negative?

##### 4 Answers

#### Answer:

**can not** have **roots both negative.**

#### Explanation:

Let

Now, we know that, if

eqn.

In our case, then, from this, it follows that,

Knowing that, both,

Combining

We conclude that,

**can not** have **roots both negative.**

**Enjoy Maths.!**

#### Answer:

Both roots cannot be negative.

The solutions of this equation is

#### Explanation:

We need

We compare this equation to

Let's calculate the discriminant

So,

the roots of the equation are

#### Answer:

See below.

#### Explanation:

Note that

If the trinom has both roots negative then all its coefficients must be positive.

Analyzing

#### Answer:

No

#### Explanation:

More briefly, given:

#2x^2-kx+(k-2) = 0#

Note that the sum of the coefficients is

#2-k+k-2 = 0#

Hence