Question

find a cubic polynomial with the sum sum of the product of its zeros taken two at a time and product of its zeros as 3,-1,and -3 respectively

Answer 1

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Answer 2

$\huge\fbox \red{Solution:}$

Generally,

A cubic polynomial say, f(x) is of the form ax3 + bx2 + cx + d.

And, can be shown w.r.t its relationship between roots as.

⇒ f(x) = k [x3 – (sum of roots)x2 + (sum of products of roots taken two at a time)x – (product of roots)]

Where, k is any non-zero real number.

Here,

f(x) = k [x3 – (3)x2 + (-1)x – (-3)]

∴ f(x) = k [x3 – 3x2- x + 3)]

where, k is any non-zero real number.