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Use the SOLVE Process to determine the missing coefficient

of a given polynomial. P(x)=x^4 - 3x^3 +ax^2 - 6x + 14

User Randomizer
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Answer:

To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:

S: Write down the given information and identify the problem.

We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".

O: Organize the information and decide on a plan.

To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.

L: Carry out the plan.

For example, let's say we substitute x = 2 into the polynomial. We get:

P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14

= 16 - 24 + 4a - 12 + 14

= -4 + 4a + 2

= 4a - 2

We are given that P(2) = 4a - 2 = 0, so 4a = 2.

Solving for a, we get:

a = 2 / 4

= 0.5

V: Check the solution.

We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.

P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14

Substituting x = 2 and a = 0.5, we get:

P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14

= 16 - 24 + 1 - 12 + 14

= 0

Since P(2) = 0, our solution appears to be correct.

Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.

User Sheik Althaf
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