Question

write a cubic polynomial expression whose zeros are 1, 2, 3​

Answer 1

$\huge\mathbb{Answer:-}$

The required cubic polynomial is x^3 - 6x^2 - 36x - 6

$\huge\mathbb{Explanation:-}$

Consider the zeroes as @, ß and Y.

Then,

@ = 1,

ß = 2, and

Y = 3

Now,

@ + ß + Y = 1 + 2 + 3 = 6

@ßY = 1 × 2 × 3 = 6

(@ß + ßY + @Y) = 2 × 6 × 3 = 36

Hence, the required polynomial is

{x^3 - (@ + ß + Y)x^2 + (@ß + ßY + @Y)x - @ßY}

= x^3 - 6x^2 - 36x - 6