The quadratic equation ax2 + bx +c = 0 has integral coefficients, and the value of its discriminant is D. What is the smallest value of D>48 for which the solutions of this quadratic equation will be irrational? a)49 b)50 c)52 d)56 please give reason...

Dear Student

 Following is the solution of your question

The quadratic equation ax² + bx +c = 0 has integral coefficients,

Its roots are given by x =

 where ,  D is the the value of its discriminant  

Its roots are rational or irrational depending on whether D is a perfect square or not

Now 49 is  a square number so smallest number greater than 48 is 50 for which roots are irrational.

So option (b) is correct

Hope it clarifies your doubt

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Team Topperlearning