If y is one of roots of equation 4x^2+2x-1=0 Then the other root is ?

Question

Your options are 

• 3y³-4y
• 4y³-3y
• 2y³-3y

Answer 1

Surya,

 

As suggested by Kenneth S., just apply the quadratic formula and get both roots:

 

4x² + 2x - 1 = 0

 

a = 4

b = 2

c = -1

 

x = [1/(2a)] [-b ± √(b² - 4ac)] = [1/(2*4)] {-2 ± √[(2)² - 4(4)(-1)]}

 

x = (1/8)(-2 ± √20) = (1/8)(-2 ± 2√5) = (-1 ± √5) / 4

 

Now going back to the given statement that y is one of the roots:

 

Let y₁ be the other root.

 

Suppose

 

y = -b/(2a) + [√(b² - 4ac)] / 2a

 

Then

 

y₁ = -b/(2a) - [√(b² - 4ac)] / 2a

 

Do a little algebra and get

 

y₁ = y - 2{[√(b² - 4ac)] / 2a} = y - [√(b² - 4ac)] / a

 

You now have y₁ in terms of y, but what practical use does this have, when you can easily find both roots?  I have to agree with the tutors, there is something wrong with what Common Core is emphasizing!

Answer 2

strange question!  you can find both of the roots using the quadratic formula: x = (1±√5)/4, I believe (check it out).

 

Now, if you call one of these by the UNFORTUNATE name y, perhaps you can substitute into each of the available proposed answers until one fits.

 

But I have to say this is an extremely twisted, indirect, awkward and seemingly foolish question.