1
Question
Assertion :If one root is √3−√2, then the equation of lowest degree with rational coefficients x4−10x2+1=0 Reason: For polynomial equation with rational coefficients irrational roots occurs in pairs.
Assertion :If one root is √3−√2, then the equation of lowest degree with rational coefficients x4−10x2+1=0 Reason: For polynomial equation with rational coefficients irrational roots occurs in pairs.
Open in App
Solution
The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
For polynomial equation with rational coefficients irrational roots occur in pairsGiven √3−√2 then √3+√2,−√3+√2,−√3−√2 are remaining roots.Sum of roots =0Product of roots (√3+√2)(√3−√2)(−√3+√2)=+1x4−10x2+1=0 has √3−√2,√3+√2,−√3+√2,−√3−√2
Both assertion and reason are correct
For polynomial equation with rational coefficients irrational roots occur in pairs
Given √3−√2 then √3+√2,−√3+√2,−√3−√2 are remaining roots.
Sum of roots =0
Product of roots (√3+√2)(√3−√2)(−√3+√2)=+1
x4−10x2+1=0 has √3−√2,√3+√2,−√3+√2,−√3−√2
Both assertion and reason are correct
Suggest Corrections
0
Similar questions