If k is a natural number and the roots of the equation x2+ 11x + 6k=0 are rational numbers then the smallest value of k is.
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roots are rational number means
x ={ b ± √D }/2a are in the form of P/Q where Q ≠ 0
this is possible only when ,
Discriminant is perfect square
e.g D = { ( 11)² -4 × 6K } is perfect square
=(121 -24k ) is a perfect square
for smallest value of K Discriminant is perfect square . e.g when we put K = 3
then D = 121 -72 = 49 this is perfect square so ,
smallest value of K = 3
Note :- K =0 possible but K is natural number so , this is not possible .
x ={ b ± √D }/2a are in the form of P/Q where Q ≠ 0
this is possible only when ,
Discriminant is perfect square
e.g D = { ( 11)² -4 × 6K } is perfect square
=(121 -24k ) is a perfect square
for smallest value of K Discriminant is perfect square . e.g when we put K = 3
then D = 121 -72 = 49 this is perfect square so ,
smallest value of K = 3
Note :- K =0 possible but K is natural number so , this is not possible .
mysticd:
you can take discriminant
the first part is unnecessary
actually i show this how roots are rational number . so i think this accessory
in quadratic equation def contains a is not equal to zero
in p/q , q means 2a , which is already defined as a not equal to zero
okay sir , send edit option i eject it ,
:-)
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4
Answer:
Step-by-step explanation:
roots are rational number means
x ={ b ± √D }/2a are in the form of P/Q where Q ≠ 0
this is possible only when ,
Discriminant is perfect square
e.g D = { ( 11)² -4 × 6K } is perfect square
=(121 -24k ) is a perfect square
for smallest value of K Discriminant is perfect square . e.g when we put K = 3
then D = 121 -72 = 49 this is perfect square so ,
smallest value of K = 3
Note :- K =0 possible but K is natural number so , this is not possible .
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