The coefficient of $x^3$ in the cubic polynomial, $\mathrm{f}(x)$, is $3$. Given that the root

Question

The coefficient of $x^3$ in the cubic polynomial, $\mathrm{f}(x)$, is $3$. Given that the roots of the equation, $\mathrm{f}(x)=0$, are $-5$, $2p$ and $p$, find an expression for $\mathrm{f}(x)$ in terms of $p$.[2] Given also that the coefficient of $x$ is $-21$, find the possible value(s) of $p$.[3]

Accepted Answer

(i) f(x) = 3(x+5)(x-2p)(x-p), (ii) p = 7 or p = 1/2

Polynomials, Cubic Equations and Partial Fractions - Forming Polynomials from Roots and Factors

Polynomials, Cubic Equations and Partial Fractions - Forming Polynomials from Roots and Factors

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