Question

The roots of the equation \[2{x^2} + 3x + 2 = 0\] are
A. real, rational and equal
B. real, rational and unequal
C. real, irrational and unequal
D. non real (imaginary)

Answer 1

Hint: Use the coefficients of the quadratic equation and their relation to determine whether the roots are real-equal, real-unequal or imaginary by checking if the relation is greater than, equal to or less than 0. Also, in order to check if the roots are rational or not, try finding the roots of the quadratic equation by factorization.

Complete step-by-step answer:
Given, the quadratic equation \[2{x^2} + 3x + 2 = 0\]
Here, \[a = 2,b = 3,c = 2\]
In order to check if the roots are real-equal, real-unequal or imaginary we need to find the relation \[{b^2} - 4ac\]
\[ \Rightarrow 9 - 16 = - 7 < 0\]
Now, \[{b^2} - 4ac < 0\]
Which implies the roots are imaginary
Therefore, option D is correct.

Note: If \[{b^2} - 4ac > 0\] then the roots would have been real and unequal and if \[{b^2} - 4ac = 0\] then the roots would have been real and equal.