Question

write the quadratic polynomial having zeros 1 and -2​

Answer 1

Answer:

x^2-x-2=0 is the quadratic equation.

Step-by-step explanation:

(x-1)(x+2)=0

x(x+2)-1(x+2)=0

x^2+2x-x-2=0

x^2-x-2=0

Answer 2

The quadratic polynomial having zeros 1 and -2 is x² + x - 2.

Procedure:

→The roots of the quadratic polynomial are 1 and -2.

Hence, the sum of roots = α + β = 1 + (-2) = -1

      The product of roots = αβ = (1)(-2) = -2

The quadratic polynomial will be: x² - (sum of roots)x + (product of roots)

Quadratic Polynomial: x² - (α + β)x + (αβ)

                                     → x² - (-1)x + (-2)

                                      →x² + x - 2

Hence, the quadratic polynomial having zeros 1 and -2 is x² + x - 2

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