How to find discriminant of non-quadratic? (1 Viewer)

[enigma_1]

Eg 9x^2 - 9x^4 -4 =0


Is it possible? I need to show that this thing has no solutions

 

[rumbleroar]

9x^2 - 9x^2 -4 =0

...doesnt that not work bc its like -4=0 ????

 

[Carrotsticks]

Eg 9x^2 - 9x^2 -4 =0


Is it possible? I need to show that this thing has no solutions

Haha that expression means nothing because for all X, the LHS is equal to -4, which is never equal to zero. Hence there are no solutions.

 

[enigma_1]

Haha that expression means nothing because for all X, the LHS is equal to -4, which is never equal to zero. Hence there are no solutions.

oh wait!! I wrote the question wrong can you check it again sorry

 

[Carrotsticks]

Re-arrange.

9x^4 - 9x^2 + 4 = 0

This is a 'hidden quadratic' 9u^2 - 9u + 4 = 0, where u=x^2.

This quadratic has discriminant 81-4(9)(4), which is negative.

Hence, 9u^2 - 9u + 4 = 0 has no solutions and thus the original equation has no solutions.

 

[braintic]

This is a 'hidden quadratic'

Perhaps a better description is that it is a quadratic in x^2.

 

[enigma_1]

Omg how did I not notice thanks everyone!

 

[Ikki]

Re-arrange.

9x^4 - 9x^2 + 4 = 0

This is a 'hidden quadratic' 9u^2 - 9u + 4 = 0, where u=x^2.

This quadratic has discriminant 81-4(9)(4), which is negative.

Hence, 9u^2 - 9u + 4 = 0 has no solutions and thus the original equation has no solutions.

No 'real' solutions ^_^
But yeah that's called reducible to quadratics.

 

[Carrotsticks]

No 'real' solutions ^_^
But yeah that's called reducible to quadratics.

Yep, no 'real' solutions =)

But since OP is asking a question of this level, I highly doubt that they would care for technicalities like that. I'd rather not confuse them.