Chapter 4: Q. 102 (page 211)

Is $\frac{1}{3}$ a zero of $f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1$ ? Explain.

Short Answer

Expert verified

$\frac{1}{3}$ is not a zero of functionlocalid="1646143603596" $f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1$ becouse $f (\frac{1}{3}) \neq 0$

Step by step solution

Step 1. Given data

The given function is

$f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1$

Zero of the function is $\frac{1}{3}$

Step 2. Verification

Substitute $\frac{1}{3}$ for x in the function

role="math" localid="1646143292347" $f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1 f (\frac{1}{3}) = 4 {(\frac{1}{3})}^{3} - 5 {(\frac{1}{3})}^{2} - 3 (\frac{1}{3}) + 1 f (\frac{1}{3}) = - 0.04 f (\frac{1}{3}) \neq 0$

$\frac{1}{3}$ is not equal to zero so $\frac{1}{3}$ is not a zero of the function

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Is $\frac{1}{3}$ a zero of $f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1$ ? Explain.

Short Answer

Step by step solution

Step 1. Given data

Step 2. Verification

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Is $\frac{1}{3}$ a zero of $f (x) = 4 x^{3} - 5 x^{2} - 3 x + 1$ ? Explain.