What kind of roots does the quadratic equation $$5x^2 + 7x + 4 = 0$$​ have?

Correct option is A

Given:

Given quadratic equation = $$5x^2 + 7x + 4 = 0$$​​

Formula Used:

For finding the nature of roots we use determinant D = $$b^2 - 4ac$$​ for any equation in form of $$ax^2 +bx +c = 0$$​​

If D =0 then real and equal roots

If D<0 then roots are imaginary or no real roots

If d>0 then roots are real and distinct

Solution:

Here in the equation $$5x^2 + 7x + 4 = 0$$​​

Here a =5 , b=7 and c = 4

So D =$$(7)^2 - 4(5)(4) = 49 - 80 = -31$$​​

Hence D = -31 < 0

So the roots are imaginary or no real roots

Hence option (a) is correct