Question

if alpha and beta are the zeros of the quadratic polynomial FX = 2 x square - 1, find the quadratic polynomial whose zeros are 2alpha upon beta and 2beta upon alpha ​

Answer 1

Given:-

Polynomial F(x) = 2x²-1

Roots are, α and β

To find :-

Quadratic Polynomial whoses zeroes are 2α/β and 2β/α .

Answer :-

x²-4x-2

Step By Step Explaination :-

F(x) = 2x²-1

Roots are α and β.

Actually the roots are ±1/√2

Quadratic Polynomia with roots as stated above are In the Attachment I have added for you!

Basically the basic Rules is,

=> x²-(α+β)x+αβ

Since we have given the α and β,we can find them,

well,Also,

=> α²+β²= (α+β)²-2αβ

Here, α+β=0 and αβ= -1/2

Rest you can see in the Attachment!!

Answer 2

Therefore new polynomial will be,

${x}^{2} - 4x - 2$

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