Polynomials

Concept: For a quadratic polynomial , if and are its zeroes, then:
Sum of zeroes:
Product of zeroes: Step 1: Rewrite the polynomial in standard quadratic form The given polynomial is . Expand and rearrange: Comparing this with : Here, , , and . Step 2: Use Vieta's formulas for sum and product of zeroes For : Sum of zeroes: . Product of zeroes: . Step 3: Use the given condition Expand the given condition: This can be written as: Step 4: Substitute the expressions for sum and product of zeroes into this equation We have: Substitute these into : Simplify the equation: The terms and cancel out: Step 5: Solve for C So, .