Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zero of $- 5$ having multiplicity 2 and zero of 10 having multiplicity $1 ; P ( 0 ) = - 250$
A) $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 250$
B) $P ( x ) = x ^ { 3 } - 75 x - 250$
C) $P ( x ) = x ^ { 3 } - 75 x ^ { 2 } - 250$
D) $P ( x ) = x ^ { 3 } + x ^ { 2 } - 75 x - 250$

Question

Quizplus · Accepted Answer

The polynomial can be expressed as $P(x) = a(x + 5)^2(x - 10)$. Given $P(0) = -250$, substituting $x = 0$ gives $-250 = a(5)^2(-10)$. Solving for $a$ gives $a = 1$. Thus, $P(x) = (x + 5)^2(x - 10) = x^3 - 75x - 250$.

Find a Polynomial of Degree 3 with Real Coefficients That −5- 5−5

Find a Polynomial of Degree 3 with Real Coefficients That $- 5$