Sum of two natural number is always natural number
2+3=5 1+11=12
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Sum and product of roots/zeroes
Sum and Product of roots/zeroes of a polynomial- Standard quadratic equation of a polynomial is ax 2 +bx+c=0, where a, b,c is constant. Let α and β are roots of a polynomial then factors are (x- α ) (x- β) = 0 x 2 -xβ-xα+αβ=0 x 2 -x(α+β) +αβ=0 Compare standard equation of polynomial then α+β= - b/a = - coefficient of x/coefficient of x 2 αβ = c/a = constant term/coefficient of x 2 Q.1. The roots of the equation x²-2x+3=0 are α and β. What is the equation whose roots are α², β²? Ans. Let α and β are the roots of the equation x²-2x+3=0 then sum and product of the roots α+β= - b/a = - coefficient of x/coefficient of x²=-(-2)/1=2 αβ = c/a = constant term/coefficient of x² =3/1=3 then