Question

Find the quadratic polynomial whose sum of zeros and product of zeros are respectively to 1 by 4 and 1 by 4 respectively

Answer 1

given, sum of zeros of quadratic polynomial = 1/4

product of zeros of quadratic polynomial = 1/4

we know, a polynomial is written as

x² - (sum of zeros)x + product of zeros.

= x² - (1/4)x + (1/4)

= 4[x² - (1/4)x + (1/4) ]

= 4x² - x + 1

hence, required polynomial is 4x² - x + 1

verification : sum of zeros = -coefficient of x/coefficient of x²

= -(-1)/4 = 1/4

product of zeros = constant/coefficient of x² = 1/4

hence, 4x² - x + 1 is correct .