Question

Does there exist a quadratic equation whose coefficients are rationals but both of its roots are irrational? why ?

Answer 1

yes i guess.
well,the irrational roots depends on the underroot part of the fomula and the underroot wont remove unless its a perfect square.
To find the root of the quadratic eqn,we use the formula:
x=[a+-sqrt(b^2-4ac)]/2*a
In this eqn:b^2-4ac is the term which decides whether the root will be irrational or not.
If,for example,the value of this term comes out to be 4 or 16 or any perfect square then the root part will be removed and the roots will become rational.
BUT if this term comes out to be 2 or 5 or some number that isnt a perfect square then the roots will be irrational.
So answer to ur qn is yes,its possible to get irrational roots with rational coefficients.