Question

find the quadratic polynomial sum and product of whose zeros are negative 1 and negative 20 respectively also find the zeros of the polynomial so obtained please answer fast

Answer 1

Answer :

Let the quadratic be ax^2 + bx + c = 0      ........(1)

Sum of roots of a quadratic = -b/a

Sum given = -1

=> -b/a = -1

     b = a

Product of roots of the quadratic = c/a

product given = -20

=>  c/a = -20

     c = -20 a

Putting the values of a and b in equation 1

ax^2 + ax + (-20 a) = 0

ax^2 + ax -20 a = 0

x^2 + x - 20 = 0 is the required quadratic.

Splitting the middle term

x^2 +5x - 4x -20 = 0

x = -5, 4 are the required roots/ zeros of the quadratic.