21)Determine the nature of the roots for the following quadratic equations \(15x^2 + 11x + 2 = 0\)

21)Determine the nature of the roots for the following quadratic equations \(15x^2 + 11x + 2 = 0\)

Answer: \(15x^2 + 11x + 2 = 0\) comparing with \(ax^2 + bx + c = 0\).

Here a = 15, b = 11, c = 2.

Discriminant \(\Delta = b^2 - 4ac\)

\(= 11^2 - 4(15)(2)\)

\(= 121 - 120\)

\(= 1 > 0\)

∴ The roots are real and unequal.