Forming a Quadratic Polynomial When Zeroes are Given


 
 
Concept Explanation
 

Forming a Quadratic Polynomial When Zeroes are Given

Forming a Quadratic Polynomial When Zeros are Given:

For  a quadratic whose zeros are large alpha and large beta, the two factors arelarge (x-alpha) and large (x-beta), so the quadratic can be obtained as the product of the two factors

large f(x)=(x-alpha) (x-beta)

          large =x^2-xbeta-xalpha+ alphabeta

         large =x^2-(alpha+beta)x+ alphabeta

         large =x^2- Sx+ P where large S=alpha+beta ;and; P= alphabeta

Example: Form a quadratic polynomial whose zeros are 4 and 5

S= 4+5 = 9

P= 4 X 5 = 20

So the quadratic is

large x^2-9x+20

Example: Form a quadratic polynomail with rational coefficients and one of whose zero is large (2+sqrt3)

Solution:  As the quadratic polynomail has rational coefficients, so the zeros will be in conjugate pairs. The other zero will be large (2-sqrt3)

large S= (2+sqrt3)+(2-sqrt3) = 4

large P= (2+sqrt3)(2-sqrt3) = (2^2-(sqrt3)^2) =4 -3= 1

So the quadratic is

large x^2-4x+1

 
 
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