You are Here: Home >< A-levels

# number or roots maths question watch

1. Im stuck on this economics entrance question, it says:
How many real roots does the equation (x^4) - (4x^3)+(4x^2)-10=0 have?

I tried differentiation but have no idea where to go from there.
The options are 0,1,2,3,4(the answer is 2)
2. (Original post by bruh2132)
Im stuck on this economics entrance question, it says:
How many real roots does the equation (x^4) - (4x^3)+(4x^2)-10=0 have?

I tried differentiation but have no idea where to go from there.
The options are 0,1,2,3,4(the answer is 2)
Also another question I'm struggling with says for
what values of a does the quadratic ax^2+(a-2)x=2 have distinct real roots-

I have found the discriminant equation and it only has one root so I put there are no values of a but the answers says a is not 2
3. you can look at it graphically:

write it as

(x2 + 2 )2 - 14 - 4x3 = 0

(x2 + 2 )2 = 14 + 4x3

the LHS is a U shape with y intercept ( 0,4 )

the RHS is a cubic with a point of inflexion at ( 0, 14 )

the curves intersect twice...
4. (Original post by the bear)
you can look at it graphically:

write it as

(x2 + 2 )2 - 14 - 4x3 = 0

(x2 + 2 )2 = 14 + 4x3

the LHS is a U shape with y intercept ( 0,4 )

the RHS is a cubic with a point of inflexion at ( 0, 14 )

the curves intersect twice...

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 26, 2017
Today on TSR

### University open days

• University of Warwick
Sat, 20 Oct '18
• University of Sheffield
Sat, 20 Oct '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 20 Oct '18
Poll

## All the essentials

### Student life: what to expect

What it's really like going to uni

### Essay expert

Learn to write like a pro with our ultimate essay guide.

### Create a study plan

Get your head around what you need to do and when with the study planner tool.

### Resources by subject

Everything from mind maps to class notes.

### Study tips from A* students

Students who got top grades in their A-levels share their secrets