Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) -1/4, 1/4

Answer 1

Let a,b be the zeros

Given sum of zeros {a+b= -1/4} and {ab=1/4}

the required quadratic equation is

x²-(a+b)x+ab=0

x²-(-1/4)x+1/4=0

x²+x/4+1/4=0

4x²+x+1=0