To solve the equation [tex]\(2x^2 - 21x + 27 = 0\)[/tex], we can start by using its factored form, which is given as [tex]\((2x - 3)(x - 9) = 0\)[/tex]. To find the roots of the equation, we need to set each factor equal to zero and solve for [tex]\(x\)[/tex]. Here are the steps:
1. Take the first factor [tex]\(2x - 3\)[/tex] and set it equal to zero:
[tex]\[
2x - 3 = 0
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
[tex]\[
2x = 3 \implies x = \frac{3}{2}
\][/tex]
3. Take the second factor [tex]\(x - 9\)[/tex] and set it equal to zero:
[tex]\[
x - 9 = 0
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 9
\][/tex]
Based on these steps, the equations that should be solved to find the roots are:
B. [tex]\(x - 9 = 0\)[/tex]
D. [tex]\(2x - 3 = 0\)[/tex]
Therefore, the correct choices are B and D.
