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,-1and-3 respectively​

Answer 1

Answer:

Let, the zeroes be

• α + ß + γ = 3
• αß + ßγ + αγ = - 1
• αßγ = - 3

General form of cubic polynomial is

✒ x³ - (α + ß + γ)x² + (αß + ßγ + αγ)x - αßγ = 0

➡ x³ - (3)x² + (-1)x - (-3) = 0

➡ x³ - 3x² - x + 3 = 0

∴ The polynomial is “ x³ - 3x² - x + 3 = 0 ”

Step-by-step explanation:

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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.