Sunday, March 31, 2013

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

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