the sum of the two roots of a quadratic equation is 5 and sum of their cubes is 35 find the equation
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x2−5x+6 is the equation
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(a+b)³=a³+b³+3ab(a+b)
a³+b³=(a+b)³-3ab(a+b)
let the roots of our equation are a,b
we have sum of roots
a+b= 5. (eq1)
and
a³+b³=35
AND
using the above relation we can find the product of roots of the equations.
35=(5)³-3ab(5)
35=125-15ab
15ab=90
ab=6. (eq2)
HENCE Product of the roots of the equation.
using both equations 1 and 2
the required equation with the sun of roots 5 and product of roots 6.
ANSWER x²-5x+6=0
AND ONE MORE THING IF YOU LIKE THE ANSWER DON'T FORGET TO HIT THE BRILLIANT BUTTON.
a³+b³=(a+b)³-3ab(a+b)
let the roots of our equation are a,b
we have sum of roots
a+b= 5. (eq1)
and
a³+b³=35
AND
using the above relation we can find the product of roots of the equations.
35=(5)³-3ab(5)
35=125-15ab
15ab=90
ab=6. (eq2)
HENCE Product of the roots of the equation.
using both equations 1 and 2
the required equation with the sun of roots 5 and product of roots 6.
ANSWER x²-5x+6=0
AND ONE MORE THING IF YOU LIKE THE ANSWER DON'T FORGET TO HIT THE BRILLIANT BUTTON.
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