Question

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

Answer 1

We have a formulla to find quadratic equation
sum of zeroes= 1 BY 4 &
product of zeroes= -1
By using formulla
x sq. -(sum of zeroes)x+ (product of zeroes)
x sq. (1 by 4) + (-1)
x sq.- 1 by 4x - 1
multiply both sides of 4
4(xsq.-1 by 4x-1)
4x sq. -1x_4

Answer 2

The quadratic polynomial with sum and product of roots 1/4 and -1 respectively is $x^{2} - \frac{1}{4}x - 1$

• Let the roots be a,b.
• Then equation of polynomial is given by

                      $x^{2} - (a+b)x + ab$  --------------(1)

Given,

          sum of roots = 1/4

                a + b        = 1/4

          product of roots = -1

                           ab       = -1

Substituting above values in (1)

∴ Equation of required polynomial is

                     $x^{2} - \frac{1}{4}x - 1$