Q - Reducible to quadratics :D (1 Viewer)

[Smile12345]

Hello All...

Could someone please help me with the following questions?

Solve....
Q1. x^4 - 7x^2 - 18 = 0

Here is my working...
a= x^2 and a^2 = (x^2)^2

a^2 - 7a - 18 = 0

(a-9)(a+2) = 0

a = 9, -2

Now... why do we only use a = 9 to get the two results +3 and -3 ???

Solve...
Q2. (x^2 - x)^2 + (x^2 - x) - 2 = 0 giving exact values

My Working....
a = x^2 - x

So a^2 + a - 2 = 0

(a - 1)(a + 2) = 0
a = 1, -2

Then what do I do.... ?
___

Thanks for your help in advance.

 

[HeroicPandas]

Q1.

a = 9
x^2 = 9
x = -3, 3

Now,
a = -2
x^2 = -2
x = √-2

Is it possible to square root a negative number?

Q2.
a = 1, -2

U let a = x^2 - x

Since a = 1, -2

Therefore, x^2 - x = 1, -2

x^2 - x = 1
x^2 - x = -2

Solve these 2 quadratics to get ur answer

 

[Smile12345]

Q1.

x = √-2

Is it possible to square root a negative number?

No, it's not possible to square root a negative number... Thanks heaps for reminding me of this!

Sorry... Can you show me how to solve the first quadratic and I'll have a go at the second...

 

[iheartOJ]

try using the quadratic formula

 

[Smile12345]

try using the quadratic formula

And instead of just doing it in the calculator.... Simplify it so I get exact values???

 

[iheartOJ]

Spot on!

It should give you the correct answer

 

[Smile12345]

Spot on!

It should give you the correct answer

Uh ha... Good..

When I do the first one I get (1 +- √5)/2

 

[Smile12345]

But the second one isn't in the answers... Should it be?

 

[HeroicPandas]

x^2 - x + 2 = 0

Explain why this quadratic is impossible to solve (or impossible to find real roots)

 

[iheartOJ]

But the second one isn't in the answers... Should it be?

There shouldn't be a second answer. This is because the number under the root is a negative, hence no real root exists (i.e. no answer exists). Have a look at your work using the discriminant

(gave you a hint before, "answer" with no 's')

 

[Smile12345]

There shouldn't be a second answer. This is because the number under the root is a negative, hence no real root exists (i.e. no answer exists). Have a look at your work using the discriminant

(gave you a hint before, "answer" with no 's')

Awe yeah, thanks for your hint... ;D

 

[Smile12345]

x^2 - x + 2 = 0

Explain why this quadratic is impossible to solve (or impossible to find real roots)

Because the number under the root is negative... We can't square a negative number...

Thanks Herioc. Tried to +1 but couldn't!

 

[HeroicPandas]

Because the number under the root is negative... We can't square a negative number...

Thanks Herioc. Tried to +1 but couldn't!

Yes

You may solve quadratics like i do:

1. Find discriminant (the key of life!)
2. Sub into quadratic formula

Most people sub it all in quadratic formula and realise the number under root is -ve and have wasted their time, whereas people who do DELTA first, can move onto the next question

 

[iheartOJ]

Yes

You may solve quadratics like i do:

1. Find discriminant (the key of life!)
2. Sub into quadratic formula

Most people sub it all in quadratic formula and realise the number under root is -ve and have wasted their time, whereas people who do DELTA first, can move onto the next question

+ 1

Good tip!

 

[Smile12345]

Yes

You may solve quadratics like i do:

1. Find discriminant (the key of life!)
2. Sub into quadratic formula

Most people sub it all in quadratic formula and realise the number under root is -ve and have wasted their time, whereas people who do DELTA first, can move onto the next question

Thanks... The best way to solve them... Yes, the discriminant is like the key of life!

 

[Smile12345]

+ 1

Good tip!

I agree...