If the product of the zeroes of the quadratic polynomial $5x^2 + 7x + k$ is $- \frac{2}{5}$, then the value of k is :

Step 1: Identify coefficients of the quadratic polynomial

A general quadratic polynomial is given by $ax^2 + bx + c$. We need to compare the given polynomial $5x^2 + 7x + k$ with this general form to identify the coefficients $a$, $b$, and $c$.

Step 2: State the formula for the product of zeroes

For a quadratic polynomial $ax^2 + bx + c$, the product of its zeroes (roots) is given by the formula $\frac{c}{a}$. This is a fundamental property of quadratic equations.

Step 3: Substitute the given values into the formula

From the given polynomial $5x^2 + 7x + k$, we have $a=5$ and $c=k$. We are also given that the product of the zeroes is $- \frac{2}{5}$. Substituting these values into the formula for the product of zeroes, we get the equation $\frac{k}{5} = -\frac{2}{5}$.

Step 4: Solve for k

To find the value of $k$, we need to solve the equation $\frac{k}{5} = -\frac{2}{5}$. We can multiply both sides of the equation by 5 to isolate $k$.

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