Polynomials and quadratic equations

Level 1

Determine the quadratic equation whose roots are 20 20 and 25 25 .

x 2 − 45 x + 500 x^2-45x+500 x 2 + 60 x + 900 x^2+60x+900 x 2 + 55 x + 400 x^2+55x+400 x 2 + 40 x + 500 x^2+40x+500

Tahmid Chowdhury by Tahmid Chowdhury , 23, Bangladesh

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1 solution

Tahmid Chowdhury
May 15, 2016

If a , b a,b are the two roots of a quadratic equation a x 2 + b x + c = 0 ax^2+bx +c=0 , then the formula for the equation is x 2 − ( a + b ) x + a b = 0 x^2 -(a+b)x+ab=0 . If ( a , b ) = ( 20 , 25 ) (a,b)=(20,25) , we get from the formulae:

x 2 − ( 20 + 25 ) x + ( 20 ) ( 25 ) = x 2 − 45 x + 500 , x^2-(20+25)x+(20)(25)=x^2-45x+500,

which is the required equation.

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