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

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

(i)1/4 , -1 (ii) √2 , 1/3 (iii) 0, √5 (iv) 1,1 (v) -1/4 ,1/4 (vi) 4,1

Solution

(i)1/4 , -1

Now formula of quadratic equation is

           

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

           

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

           

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

           

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

           

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

           

Plug the value in formula we get

                                    x² –(4)x  + 1 = 0

x²–4x  + 1 = 0