Chapter 11: Q. 426 (page 1069)

Use the Zero Product Property in following exercises, solve.
$3 m (2 m - 5) (m + 6) = 0$

Short Answer

Expert verified

The solutions for the given expression are $m = 0, \frac{5}{2} a n d - 6$ .

Step by step solution

Step 1. Given and explanation.

We have $3 m (2 m - 5) (m + 6) = 0$ .

We know that the zero product property states that if $a \times b = 0$ , then either of the factors, both are equal to zero.

So putting them equal to zero will give us the values.

Step 2. Evaluating the values.

We have $3 m (2 m - 5) (m + 6) = 0$ .

Putting them equal to zero gives us,

$3 m = 0 m = 0$

$2 m - 5 = 0 2 m = 5 m = \frac{5}{2}$

$m + 6 = 0 m = - 6$

This shows that values are $0, \frac{5}{2} a n d - 6$ .

Step 3. Check the solution.

We will check the solution by putting the value of the solution in the equation separately. If the equation satisfies, our answer is right.

When $m = 0$
$[3 (0)] [2 (0) - 5] [(0) + 6] = 0 (0) (0 - 5) (6) = 0 0 = 0$
Hence satisfied.
When $m = \frac{5}{2}$
$[3 (\frac{5}{2})] [2 (\frac{5}{2}) - 5] [(\frac{5}{2}) + 6] = 0 (\frac{15}{2}) (5 - 5) (\frac{17}{6}) = 0 (\frac{15}{2}) (0) (\frac{17}{6}) = 0 0 = 0$
Hence satisfied.
When $m = - 6$
$[3 (- 6)] [2 (- 6) - 5] [(- 6) + 6] = 0 (- 18) (- 12 - 5) (0) = 0 (- 18) (- 17) (0) = 0 0 = 0$
Hence satisfied.

Thus our calculations are right.

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Use the Zero Product Property in following exercises, solve.
$3 m (2 m - 5) (m + 6) = 0$

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Evaluating the values.

Step 3. Check the solution.

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Use the Zero Product Property in following exercises, solve.3m(2m-5)(m+6)=0

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Evaluating the values.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use the Zero Product Property in following exercises, solve.
$3 m (2 m - 5) (m + 6) = 0$