Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
√2,13
Sum of zeros =√2
Product of zeros =13
Let the polynomial be ax2+bx+c, and its zeroes be α and β.
α+β=√2.
αβ=13
∴ Quadratic polynomial =x2−(Sum of zeroes)x+(Product of zeros)
=x2−√2x+13
=13[3x2−3√2x+1]
∴ Quadratic polynomial is 3x2−3√2x+1.