Solve the following question.
(ii) For the quadratic equation `m^2+5m-14=0`, check whether m=3 and m=-7 are the roots or not ?

Answer

To determine whether \( m = 3 \) and \( m = -7 \) are roots of the quadratic equation \( m^2 + 5m - 14 = 0 \), we will substitute these values into the equation and check if the equation holds true (i.e., if it equals zero).

### Step 1: Substitute \( m = 3 \) into the equation

We start by substituting \( m = 3 \) into the equation:

\[ m^2 + 5m - 14 = 0 \]

Substituting \( m = 3 \):

\[ 3^2 + 5(3) - 14 = 0 \]

Calculating the left-hand side:

\[ 9 + 15 - 14 = 0 \]

Now, simplifying:

\[ 9 + 15 = 24 \quad \text{and} \quad 24 - 14 = 10 \]

So, we have:

\[ 10 \neq 0 \]

### Conclusion for \( m = 3 \)

Since substituting \( m = 3 \) does not yield zero, we conclude that \( m = 3 \) is **not a root** of the equation.

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### Step 2: Substitute \( m = -7 \) into the equation

Next, we substitute \( m = -7 \) into the equation:

\[ m^2 + 5m - 14 = 0 \]

Substituting \( m = -7 \):

\[ (-7)^2 + 5(-7) - 14 = 0 \]

Calculating the left-hand side:

\[ 49 - 35 - 14 = 0 \]

Now, simplifying:

\[ 49 - 35 = 14 \quad \text{and} \quad 14 - 14 = 0 \]

So, we have:

\[ 0 = 0 \]

### Conclusion for \( m = -7 \)

Since substituting \( m = -7 \) yields zero, we conclude that \( m = -7 \) **is a root** of the equation.

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### Final Summary

- \( m = 3 \) is **not a root** of the equation \( m^2 + 5m - 14 = 0 \).
- \( m = -7 \) **is a root** of the equation \( m^2 + 5m - 14 = 0 \).

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