Q11. If px=2x3+6x-12聽and聽qx=5x2+4 t... [FREE SOLUTION]

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

Subtract (2) from (1) gives,

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

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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91影视

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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91影视

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

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Geometry

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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