# For what values of k will the equation have no real roots?

2x^2-3x+kx=-1/2

1. k<1 or k>1
2. 1<=k<=5
3. k<=1 or k>=5
1<k<5

b^2-4ac
a=2 b=3 c=k

## The Attempt at a Solution

(3)^2-4(2)(k)
=9-8k<0
=9/8<k
=1&1/8<k

I get the answer above but don't know how it relates???
Any insight would be appreciated.

Thank you,
Jaco

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MarcusAgrippa
Gold Member
Find the discriminant of your quadratic equation. The equation has no real roots if the discriminant is less than zero.

jbriggs444
Homework Helper
2019 Award

2x^2-3x+kx=-1/2

## Homework Equations

b^2-4ac
a=2 b=3 c=k
Look at the original equation again.

What is the coefficient on x? What is the constant term?

MarcusAgrippa
Gold Member

Jbriggs,
I have been looking at other threads and found a similar example and there:
(-3)^2-4(2)(k+1/2)
=-9-8k+4
=-5-8k
=> k=5/8
Thank you for pointing that out Marcus

Is this correct?

MarcusAgrippa
Gold Member
It doesn't look correct. What is the general form of a quadratic equation? Write your equation in a way that imitates that general form and identify correctly the values of a,b,c. Then write down the general definition of the discriminant, and substitute your values of a,b,c into it. The solve the inequality (discriminant) < 0 for k.

• Jaco Viljoen and jbriggs444
SammyS
Staff Emeritus
Homework Helper
Gold Member

2x^2-3x+kx=-1/2

1. k<1 or k>1
2. 1<=k<=5
3. k<=1 or k>=5
1<k<5

b^2-4ac
a=2 b=3 c=k

## The Attempt at a Solution

(3)^2-4(2)(k)
=9-8k<0
=9/8<k
=1&1/8<k

I get the answer above but don't know how it relates???
Any insight would be appreciated.

Thank you,
Jaco
Please restate the entire problem as it was given to you.

You may have a typo in the quadratic expression as you posted it. If it's correct as it is, then you still do not have the correct b or c .

Sammy,
For what values of k will the equation 2x^2 -3x + kx = -1/2 have no real roots?

1. k<1 or k>1
2. 1<=k<=5
3. k<=1 or k>=5
1<k<5

jbriggs444
Homework Helper
2019 Award
Everyone responding to this thread is attempting to point out that the b and c that you have harvested from that equation are wrong.

ok, I have been considering this too as:
(3x+kx)^2-4(2)(-1/2)
(3x+kx)(3x+kx)+4
9x^2+3kx^2+3kx^2+k^2x^2
9x^2+6kx^2+k^2x^2

jbriggs444
Homework Helper
2019 Award
Re-read post #7 above. What is the standard form for a quadratic equation? Can you restate the original equation in that form?

ax^2+bx+c=0
2x^2+(3x+kx)+1/2=0
2x^2+3x+kx=-1/2
kx=-1/2-2x^2-3x
k=(1/2-2x^2-3x)/x

wow, i feel more confused...

SammyS
Staff Emeritus
Homework Helper
Gold Member
ax^2+bx+c=0
2x^2+(3x+kx)+1/2=0
It's good to this point.

Take the expression in parentheses and factor out x.

2x^2+(3x+kx)+1/2=0
2x^2+x(3+k)+1/2=0
2x^2+(3+k)(x+1/2)=0
2x^2+3x+1&1/2+kx+1/2k=0
kx+1/2k=-2x^2-3x-1&1/2
3/2kx=-2x+3+1&1/2
3kx=-4x+9
k=(-4x+9)/x

Last edited:
SammyS
Staff Emeritus
Homework Helper
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2x^2+(3x+kx)+1/2=0
2x^2+x(3+k)+1/2=0
Stop at this point !
2x^2+(3+k)(x+1/2)=0
2x^2+3x+1&1/2+kx+1/2k=0
kx+1/2k=-2x^2-3x-1&1/2
1&1/2k=(-2x+3+1&1/2)/x
What is the coefficient of x ?

1?

jbriggs444
Homework Helper
2019 Award
1
In the expression 2x2 + 3x + 4, what is the coefficient on the "x" term?

3

jbriggs444
Homework Helper
2019 Award
Good.

Now, in the expression 2x2 + x(3+k) + 1/2, what is the coefficient on the x term?

2x^2+1x(3+k)+1/2

1 or is it still 3?

2x^2+1x(3+k)+1/2

I am missing this, I just can't seem to get it...

Its not the 2 is it?

SammyS
Staff Emeritus
Homework Helper
Gold Member
What if we write it like this?

2x2 + (3+k)x + (1/2) = 0

What is the coefficient of x2 ?

What is the coefficient of x ?

What is the constant term ?

• Jaco Viljoen