Question

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

Answer 1

a=2andb=1
x^2-3x+2=0 is required quadratic equation

Answer 2

Hiii friend,


A + B = 3---------(1)

A - B = 1------------(2)


From equation (1) we get,


A + B = 3

A = 3-B---------(3)


Putting the value of A in equation (2)

A - B = 1

3-B - B = 1

-2B = 1-3

-2B = -2

B = -2/-2 => 1

Putting the value of B in equation (3)

A = 3-B => 3-1 = 2

Therefore,

2 and 1 are the two zeroes.


Let Alpha = 2 and beta = 1

Sum of zeroes = (Alpha + Beta) = (2+1) = 3


Product of zeroes = (Alpha × Beta) = (2 × 1) = 2


Therefore,


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


=> X² -(3)X + 2


=> X²-3X+2



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