Question

find the sum and product of zeroes of f(n)=x2-2x+3​

Answer 1

Answer:

Step-by-step explanation:

Given that  

a and b are the zeros of  

x  

2

−2x+3

Then,  

We know that  

Sum of zeros =−  

coeff. of x  

2

 

coeff. of x

​  

 

a+b=−  

+1

−2

​  

 

a+b=2−−−−−−−−(1)

Now,  

Product of zeros =  

coeff. of x  

2

 

constant term

​  

 

a.b=  

1

3

​  

 

ab=3−−−−−−−−−−−(2)

If 2a+3 and 2b+3 are the zeros of other polynomial.

Then

Sum of zeros =2a+3+2b+3

=2(a+b)+6

=2(2)+6

=10

Sum of zeros =10

Product of zeros =(2a+3)(2b+3)

=4ab+6a+6b+9

=4ab+6(a+b)+9

=4×3+6×2+9

=12+12+9

=24+9

Product of zeros =33

Now,

Equation of polynomial  

x  

2

− (Sum of zeros) x+ product of zeros =0

x  

2

−10x+33=0

Hence, this is the answer.