Chapter 7: Q11. (page 350)

If $p (x) = 2 x^{3} + 6 x - 12 and q (x) = 5 x^{2} + 4$ then find $3 p (a) - q (a + 1)$ .

Short Answer

Expert verified

The value of $3 p (a) - q (a + 1) = 6 a^{3} - 5 a^{2} + 8 a - 45$ .

Step by step solution

Step 1. Write down the given information.

The given functions are $p (x) = 2 x^{3} + 6 x - 12 and q (x) = 5 x^{2} + 4$ .

Step 2. Calculation.

Evaluating $3 p (a) - q (a + 1)$ by plugging $x = a$ in $p (x) = 2 x^{3} + 6 x - 12$ and multiply by 3 and then subtract $q (a + 1)$ by plugging $x = a + 1$ in $q (x) = 5 x^{2} + 4$ . Therefore,

role="math" localid="1648111658019" $\begin{matrix} p (x) = 2 x^{3} + 6 x - 12 .... (Given) \\ 3 p (x) = 3 (2 x^{3} + 6 x - 12) \\ 3 p (a) = 3 (2 {(a)}^{3} + 6 (a) - 12) \\ = 6 a^{3} + 18 a - 36 .... (1) \\ Now, q (x) = 5 x^{2} + 4 \\ q (a + 1) = 5 {(a + 1)}^{2} + 4 \\ = 5 a^{2} + 10 a + 9 .... (2) \end{matrix}$

Subtract (2) from (1) gives,

$\begin{matrix} 3 p (a) - q (a + 1) = (6 a^{3} + 18 a - 36) - (5 a^{2} + 10 a + 9) \\ = 6 a^{3} - 5 a^{2} + 8 a - 45 \end{matrix}$

Step 3. Conclusion.

The value of $3 p (a) - q (a + 1) = 6 a^{3} - 5 a^{2} + 8 a - 45$ .

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If $p (x) = 2 x^{3} + 6 x - 12 and q (x) = 5 x^{2} + 4$ then find $3 p (a) - q (a + 1)$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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If px=2x3+6x-12andqx=5x2+4 then find 3pa-qa+1.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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If $p (x) = 2 x^{3} + 6 x - 12 and q (x) = 5 x^{2} + 4$ then find $3 p (a) - q (a + 1)$ .