C1 Quadratic question

This is the one thing I now don't understand and need some help with.

The question is :
Find the real roots of the equation x⁴-5x² -36 = 0 by considering it as a quadratic in x²

^{I square rooted the whole thing and ended up with the wrong answer using the quadratic formula on that rooted.}

^{Help ):}

Reply 1

Kevin De Bruyne

21

Original post by Dowel

This is the one thing I now don't understand and need some help with.

The question is :
Find the real roots of the equation x⁴-5x² -36 = 0 by considering it as a quadratic in x²

^{I square rooted the whole thing and ended up with the wrong answer using the quadratic formula on that rooted.}

^{Help ):}

Let u = x^2. Then ....

Reply 2

YeezyYeezy

1

Use substitution... let k=x^2
then solve as a normal quadratic then once you've found the values for k sub them into your substitution to gain the x values

Reply 3

greg2321

1

Original post by Dowel

This is the one thing I now don't understand and need some help with.

The question is :
Find the real roots of the equation x⁴-5x² -36 = 0 by considering it as a quadratic in x²

^{I square rooted the whole thing and ended up with the wrong answer using the quadratic formula on that rooted.}

^{Help ):}

factoise like a quadratic

(x^2+4)(x^2-9)=0
X^2=0
x=3 , x= -3

to make easier, let y=x^2

(x^2)^2 - 5(x^2)-36
y^2 - 5y -36
(y+4)(y-9)
y=9
x^2 = 9
x=3 , x=-3 :smile:

Reply 4

Dowel

OP

8

Original post by greg2321

factoise like a quadratic

(x^2+4)(x^2-9)=0
X^2=0
x=3 , x= -3

to make easier, let y=x^2

(x^2)^2 - 5(x^2)-36
y^2 - 5y -36
(y+4)(y-9)
y=9
x^2 = 9
x=3 , x=-3 :smile:

This was really helpful, thanks :smile:

Reply 5

candyflossman

6

Original post by Dowel

This is the one thing I now don't understand and need some help with.

The question is :
Find the real roots of the equation x⁴-5x² -36 = 0 by considering it as a quadratic in x²

^{I square rooted the whole thing and ended up with the wrong answer using the quadratic formula on that rooted.}

^{Help ):}

Imaginary roots are x= 2i,-2i to give four coordinates.
A = (3,0,0i)
B = (-3,0,0i)
C = (0,0,-2i)
D = (0,0,2i)
Origin = (0,0,0i)

Add it for fun. Bare jokes. Like in proofs sometimes they forget to ask that.

C1 Quadratic question

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