Question

find a quadratic polynomial whose zeroes are alpha and beta satisfying the relation alpha +beta =3 and alpha -beta= -1

Answer 1

Sol : Let α and ß be the zeroes of p ( x ).

A/Q,

 α + ß = 3 ------- equation 1

 α - ß = - 1 ------- equation 2

By adding equation 1 and 2,

 α + ß + α - ß = 3 - 1

 2 α = 2

  α = 2 / 2 = 1.

By substituting the value of α in equation 1,

  α + ß = 3

  1 + ß = 3

  ß = 3 - 1

  ß = 2

Now by multiplying α and ß,

 α * ß = 2 * 1 = 2.

The formula for a quadratic equation ,

 = x² - ( α + ß ) x + α * ß

By substituting the values of ( α + ß ) and α * ß ,

 = x² - ( 3 ) x + 2

 = x² - 3 x + 2.

So , your answer is ( x² - 3 x + 2 ).

Answer 2

$the \: quadratic \: polynomial \: whose \: zeroes \: are \: \alpha \beta is$

$\alpha \beta$