Find a quadratic polynomial the sum and product of whose zeroes are √2 and-3/2 respectively

Question

Find a quadratic polynomial 

Answer 1

For a quadratic polynomial Ax² + Bx + C, the sum of the zeroes is -B/A and the product is C/A.

 

So, -B/A = √2 and C/A = -3/2.

 

One possible choice for A, B, and C is A = 2, C = -3, and B = -2√2.

 

The polynomial 2x² -2√2x - 3 meets the given requirements.