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  • Suppose a,b denote the distinct roots of the quadratic polynomial x^2+20x-2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x^2-20x+2020. then the value of ac(a-c)+ad(a-d)+bc(b-c) +bd(b-d)

Suppose a,b denote the distinct roots of the quadratic polynomial x^2+20x-2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x^2-20x+2020. then the value of ac(a-c)+ad(a-d)+bc(b-c) +bd(b-d)

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Solution:      x^2+20x-2020=0   has two  roots   a,bin R

                 Rightarrow      x^2-20x+2020=0    has two roots c,din R

              ac(a-c)+ad(a-d)+bc(b-c)+ bd(b-d)\ \ Rightarrow a^2c-ac^2+a^2d-ad^2+b^2c-bc^2+b^2d-bd^2\ \ Rightarrow a^2(c+d)+b^2(c+d)-c^2(a+b)-d^2(a+b)\ \Rightarrow (c+d)(a^2+b^2)-(a+b)(c^2+d^2)

            (c+d)[(a+b)^2-2ab]-(a+b)[(c+d)^2-2cd]\ \Rightarrow 20[(20)^2-4040]+20[(20)^2-4040]=16000

 

          

Posted by

Deependra Verma

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