Let one root of ax2+bx+c=0 where a,b,c∈Z,a≠0 be 3+√5, then the other root of the equation will be
A
√5
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B
3
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C
−3+√5
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D
3−√5
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Solution
The correct option is D3−√5 Given that one root of ax2+bx+c=0 where a,b,c are integers and a≠0 is 3+√5.
If one root of a quadratic equation with rational coefficients is irrational and of the form α+√β, then the other root must also be irrational and of the form α−√β. ∴ The other root of the equation will be 3−√5.