Question

find a quadratic polynomials each with the given as the sum and a product of its zeros respectively:- -1/√2, 2/3​

Answer 1

Answer:

x2-sx+p

x2-(-1/√2)+(2/√3)

x2+1/√2+2/√3

Answer 2

Let the polynomial be

p(x)=ax

2

+bx+c

Sum of zeroes =

2

−

a

b

=

2

Asuuming a=1

−

1

b

=

2

b=−

2

Product of zeroes =−1

a

c

=

3

1

Assuming a=1

c=

3

1

Now a=1, b=−

2

and c=

3

1

Hence, the required quadratic polynomial =ax

2

+bx+c

=x

2

−

2

x+

3

1

=3(x

2

−

2

x+

3

1

)

=3x

2

−3

2

x+1