IGCSE MATHEMATICS TOPIC : Finding a Polynomial With Given Roots

 IGCSE Maths Notes: Finding a Polynomial With Given Roots

The roots of a polynomial whereare constants are given by the solutions to. Suppose though that we have the roots and want to find the polynomial. We can form the polynomialexpand the brackets and factorise.

Example: Find the polynomial with roots 1, 3, 5.

Often the roots are surds. Still we can follow the above procedure. The algebra is much simpler if we deal with the surds first.

Example: Find the polynomial with rootsand 4.

The above method only works if the coefficient of the highest power ofis 1. We usually have to present the answers in a form where the coefficients are all integers. Suppose we are told the roots areThe expressionhas these as roots. Because of the fraction1 over 2, we should now multiple by 2 to getthen expand the brackets to get

IGCSE MATHEMATICS TOPIC : The Laws of Indices

IGCSE Maths Notes: The Laws of Indices

1. Ifso that
   
2. so that
   
3. so that
   
4. so that
   
5. so that
   
6. so that
   
7. so thatand
   
8. so that
   
9. so that
   
10. so thatIn particularso
    
11. so that
    
12. so that
    
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IGCSE MATHEMATICS TOPIC : Solving Simple Differential Equations

Simple differential equations take the formWe have to solve the equation to findas a function ofWe do this by putting all the 's on the right and integrating. Normally when we integrate we have to add a constant. We can find the value of this constant if we are told a point on the curve.

For example, dy overThe pointlies on the curve. Findas a function of

We now have to find C. We are told in the question that y=0 when x=5. Hence

Example: The point lies on the curve. Find y as a function of x.

We now have to find C. We are told in the question thatwhenHence

ExampleThe pointlies on the curve. Findas a function of

We now have to find C. We are told in the question thatwhenHence