Question

If alpha and beta are the zeros of quadratic polynomial f(x) = x^2-1 ,find a quadratic polynomial whoes zeros are 2a/b and 2b/a

Answer 1

Heya !!!

P(X) => X²-1

=> (X)² - (✓1)²

=> (X+1) (X-1) = 0

=> (X+1) = 0 OR (X-1) = 0

=> X = -1 OR X = 1

Let Alpha = -1 and Beta = 1

Sum of zeroes = Alpha + Beta = -1 + 1 = 0

And,

Product of zeroes = Alpha × Beta = -1 × 1 = -1

Sum of zeroes of Quadratic polynomial whose zeroes are 2Alpha/ Beta + 2 Beta / Alpha

=> 2Alpha² + 2Beta² / Beta × Alpha

=> 2( Alpha² + Beta²)/ -1


We know that,


(A²+B²) = (A+B)² - 2 Alpha × Beta.


So,

=> 2 × (Alpha + Beta)² - 2 × Alpha × Beta /-1

=> 2(0)² - 2 × -1/-1

=> 2/-1

And,

Product of zeroes = 2Alpha/ Beta × 2Beta/Alpha = 2 Alpha × 2 Beta / alpha × Beta

=> 2 ( -1)/-1

=> -2/-1 = 2

Therefore,

Required Quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes

=> X²-(-2/1)X + 2

=> X²+2X+2

HOPE IT WILL HELP YOU..... :-)

Answer 2

I don’t know Sorry about that