The polynomial with given roots is,
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.
What is factor of polynomial?
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
Given:
The polynomial y(x) that has roots at x = -0.7, x = 0.5, x = 3.4 and x = 5.8.
Since if 'a' is a root of the polynomial then (x - a) is the factor of the polynomial.
So, the factors of the polynomial are, (x + 0.7), (x - 0.5), (x - 3.4), (x - 5.8).
⇒ y(x) = (x + 0.7)(x - 0.5)(x - 3.4)(x - 5.8)
= (x^2 - 0.5x + 0.7x - 0.35)(x^2 - 5.8x - 3.4x + 19.72)
= (x^2 + 0.2x - 0.35)(x^2 - 9.2x + 19.72)
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902
The graph of the polynomial on the domain -1 ≤ x ≤ 6 is attached below.
Hence, the polynomial with given roots is,
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.
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