Question

use the value of the discriminant to determine the number and type of roots for each equation to answer the following questions.

$2x^2 - 7x + 9 = 0$

$\circ$ 2 real, rational

$\circ$ 2 real, irrational

$\circ$ 2 complex

$\circ$ 1 real, rational

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).
Here, \(a = 2\), \(b = -7\), \(c = 9\).

Step2: Calculate discriminant

Substitute values: \(D = (-7)^2 - 4\times2\times9\)
\(= 49 - 72\)
\(= -23\)

Step3: Analyze discriminant

Since \(D < 0\), the quadratic has 2 complex (non - real) roots (conjugate pairs).

Answer:

2 complex