Question

given the equation $3x^2 - 9x + 7 = 0$, what is the value of the discriminant and the nature of its roots? use the keypad to enter your answer in the box. additional symbols can be found using the drop - down arrows at the top of the keypad. the value of the discriminant is $square$ which indicates that the equation have $square$ roots.

Explanation:

Step1: Identify coefficients

For quadratic $ax^2+bx+c=0$, $a=3$, $b=-9$, $c=7$

Step2: Apply discriminant formula

Discriminant $D=b^2-4ac$
$D=(-9)^2-4(3)(7)$

Step3: Calculate discriminant

$D=81-84=-3$

Step4: Analyze root nature

Since $D<0$, roots are non-real (complex conjugate)

Answer:

The value of the discriminant is $-3$ which indicates that the equation have two distinct complex (non-real) roots.