Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

Question

(i) 1/4 , -1

(ii)√2 , 1/3 

(iii) 0, √5 

(iv) 1, 1 

(v) -1/4, 1/4

(vi) 4,1

Answer 1

(i)1/4, -1

Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(1/4)x -1  = 0 
Multiply by 4 to remove denominator we get
4x²  -  x  -4  = 0

(ii) √2 , 1/3 
Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(√2)x  + 1/3  = 0 
Multiply by 3 to remove denominator we get
3x²  - 3√2 x + 1  = 0

(iii) 0, √5
Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(0)x  + √5  = 0 
simplify it we get
x²   + √5  = 0

(iv) 1,1  
Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(1)x  + 1  = 0 
simplify it we get  
x²  -  x + 1  = 0 

(v) -1/4 ,1/4
Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(-1/4)x  + 1/4  = 0 
multiply by 4 we get
4x²   +  x + 1  = 0 

(vi) 4,1
Now formula of quadratic equation is
x²-(Sum of root)x + (Product of root) = 0
Plug the value in formula we get
x² –(4)x  + 1 = 0 
x² –4x  + 1 = 0