If the product of the zeroes of the quadratic polynomial 5x2+7x+k is −52, then the value of k is :
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Step-by-Step Solution
Step 1: Identify coefficients of the quadratic polynomial
A general quadratic polynomial is given by ax2+bx+c. We need to compare the given polynomial 5x2+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 ax2+bx+c, the product of its zeroes (roots) is given by the formula ac. This is a fundamental property of quadratic equations.
Step 3: Substitute the given values into the formula
From the given polynomial 5x2+7x+k, we have a=5 and c=k. We are also given that the product of the zeroes is −52. Substituting these values into the formula for the product of zeroes, we get the equation 5k=−52.
Step 4: Solve for k
To find the value of k, we need to solve the equation 5k=−52. We can multiply both sides of the equation by 5 to isolate k.