Question

Find a cubic polynomial with the sum, sum of the products of its zeroes of two at a time and product of its zeroes as 4,0 and -6 respectively ​

Answer 1

Answer:

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.