Find a quadratic polynomial with rational coefficient whose one zero is √5-2.
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Hello Jay
Great question
Always remember whenever you find a quadratic polynomial with rational coefficient whose one root is irrational,then other root will also be irrational and one root will be the conjugate of the other.For example if one root is 3+√5 then other root must be 3-√5.
In the given question one of the roots is -2+√5 then other root must be -2-√5
.Now we know the roots we can find the quadratic equation.
sum of roots=(-2+√5 )+(-2-√5)=-4
and product of roots=(-2+√5 )(-2-√5)=-1
so the quadratic equation is x²-(sum of roots)x+product of roots=0
or,x²-(-4)x-1
or,x²+4x-1=0 is the required answer
Hope it Helps
Great question
Always remember whenever you find a quadratic polynomial with rational coefficient whose one root is irrational,then other root will also be irrational and one root will be the conjugate of the other.For example if one root is 3+√5 then other root must be 3-√5.
In the given question one of the roots is -2+√5 then other root must be -2-√5
.Now we know the roots we can find the quadratic equation.
sum of roots=(-2+√5 )+(-2-√5)=-4
and product of roots=(-2+√5 )(-2-√5)=-1
so the quadratic equation is x²-(sum of roots)x+product of roots=0
or,x²-(-4)x-1
or,x²+4x-1=0 is the required answer
Hope it Helps
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