Answer:
a = 9
b = 7
Explanation:
For the given polynomial 2x³ - ax² + bx + 6 to be exactly divisible by x² - 5x + 6, it means it must also be divisible by the individual factors of x² - 5x + 6.
So let's factorize x² - 5x + 6.
Factorizing it gives us;
(x - 2)(x - 3)
Thus means that the given polynomial should be exactly divisible by either (x - 2) or (x - 3).
This means that at x = 2 or 3, the polynomial will equal zero.
Thus;
f(2) = 2(2)³ - a(2)² + b(2) + 6 = 0
16 - 4a + 2b + 6 = 0
Adding and Rearranging we have;
4a - 2b = 22
Divide through by 2 to get;
2a - b = 11 - - - (eq 1)
Similarly;
f(3) = 2(3)³ - a(3)² + b(3) + 6 = 0
54 - 9a + 3b + 6 = 0
Adding and Rearranging we have;
9a - 3b = 60
Divide through by 3 to get;
3a - b = 20 - - - (eq 2)
Subtract eq 1 from eq 2 to get;
3a - 2a - b - (-b) = 20 - 11
a = 9
Put 9 for a in eq 2 to get;
3(9) - b = 20
27 - b = 20
b = 27 - 20
b = 7
In Spanish, there is no need to change the word order. Since the problem asks for the change of this order we will use simple steps to do this. Thus, we will form Spanish questions from declarative sentences.
1) Begin with a typical declarative sentence: We start normal sentences with the subject and next follows to the verb.
2) Exchange the order of the subject and the verb: In English, when you say<em> this is...</em> in the simple form you say <em>is this...?</em> in the question form. In fact, the same happens in Spanish. So you, for example, change <em>ésta es...</em> to <em>¿es ésta...?</em> The same process also works for other sentences that don’t fit the <em>this is...</em> standard like<em> la niña es bonita</em> to <em>¿es bonita la niña?
</em>
3) Do not worry about <em>do</em>: In English, questions often include the verb<em> do</em>, but the word <em>do</em> is understood as part of the verb in Spanish.
Therefore, the change is as follows:
1. ¿Prepara la prueba la Profesora Cruz?
<em>Does the teacher Cruz prepare the test?</em>
2. ¿Necesitamos estudiar Sandra y yo?
<em>Do Sandra and I need to study?</em>
3. ¿Practican los chicos el vocabulario?
<em>Do the boys practice the vocabulary?</em>
4. ¿Termina Jaime la tarea?
<em>Does Jaime finish the homework?</em>
5. ¿Trabajas tú en la biblioteca?
<em>Do you work in the library?</em>
A.peina..............................