Chapter 4: Q. 61 (page 210)

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.
$f (x) = x^{3} + 19.5 x^{2} - 1021 x + 1000.5$

Short Answer

Expert verified

The real zeros offafter rounding it two decimal places are $1, 23, a n d - 43.5 .$

Step by step solution

Step 1. Given Information

The given function is $f (x) = x^{3} + 19.5 x^{2} - 1021 x + 1000.5$

We have to find the real zeros and round them to two decimal places.

Step 2. Finding the real zeros

The degree of the polynomial is $3$ ,thus it has three roots.

Since there are noninteger coefficients, the Rational Zeros Theorem doesn't apply.

Step 3. Determine the bounds on the zeros of f

The leading coefficient of f is $1$ with $a_{2} = 19.5, a_{1} = - 1021, a_{0} = 1000.5$

Step 4. Evaluate the expressions using the formula

So,

$M a x, {1, |19.5| + |- 1021| + |1000.5|} = M a x, {1, 2041} = 2041 1 + M a x, {|19.5|, |- 1021|, |1000.5|} = 1 + 1021 = 1022$

The smaller of two numbers, $1022$ is the bound.

Every real zero of f liesbetween $- 1022 a n d 1022 .$

Step 5. Sketch the graph of the polynomial

From the graph, we conclude that f appears to have three x-intercepts: $1, 23, a n d - 43.5 .$

And

$f (1) = 0 f (23) = 0 f (- 43.5) = 0$

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In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.
$f (x) = x^{3} + 19.5 x^{2} - 1021 x + 1000.5$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the real zeros

Step 3. Determine the bounds on the zeros of f

Step 4. Evaluate the expressions using the formula

Step 5. Sketch the graph of the polynomial

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In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.f(x)=x3+19.5x2-1021x+1000.5

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the real zeros

Step 3. Determine the bounds on the zeros of f

Step 4. Evaluate the expressions using the formula

Step 5. Sketch the graph of the polynomial

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.
$f (x) = x^{3} + 19.5 x^{2} - 1021 x + 1000.5$