Chapter 7: Q50. (page 351)

The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . For what value of x, $f (x) = 0$ .

Short Answer

Expert verified

The value ofx is $0, - 1 and 4$ for which $f (x) = 0$ .

Step by step solution

Step 1. Write down the given information.

It is given that the graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Therefore, the point $(5, 15)$ will satisfy,

$f (x) = a x (x - 4) (x + 1) . . . . (1)$

Step 2. Calculation.

Since the graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Therefore, the point $(5, 15)$ will satisfy $f (x) = a x (x - 4) (x + 1)$ .

$\begin{matrix} 15 = a (5) ((5) - 4) ((5) + 1) \\ 15 = 30 a \\ a = \frac{1}{2} \end{matrix}$

Plugging $a = \frac{1}{2}$ in (1),

localid="1648632935219" $f (x) = \frac{1}{2} x (x - 4) (x + 1) . . . . (2)$

Substitute $f (x) = 0$ in (2), to find the value of $(x)$ , for which $f (x) = 0$ . Therefore from (2),

localid="1648632951759" $\begin{matrix} (0) = \frac{1}{2} x (x - 4) (x + 1) \\ x (x - 4) (x + 1) = 0 \\ x = 0, x = - 1 and x = 4 \end{matrix}$

Step 3. Conclusion.

The value of x is $0, - 1 and 4$ for which $f (x) = 0$ .

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The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . For what value of x, $f (x) = 0$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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The graph of the polynomial function fx=axx-4x+1passes through the point 5,15. For what value of x, fx=0.

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

Geometry

Probability and Statistics

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . For what value of x, $f (x) = 0$ .