1 of 8 0-day streak

Solve a higher-degree polynomial equation or inequality

Question 1 of 8

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Consider this polynomial equation for real x

-\left(x + 5\right)\left(x - 1\right)\left(x - 2\right)^{2}\left(x - 3\right) = 0

Use exact values. Write the comparison with zero, factorise completely, and verify the real roots

Let \(F(x)\) denote the left side minus the right side of the displayed comparison. Root and multiplicity entries refer to \(F(x)=0\); enter distinct roots in increasing order. For an inequality, its final solution is the full set of inputs satisfying the original comparison

(a)1 mark

Select the valid substitution or product for the displayed polynomial

-\left(x + 5\right)\left(x - 1\right)\left(x - 2\right)^{2}=0

\left(x + 5\right)=1

-\left(x + 5\right)\left(x - 1\right)\left(x - 2\right)^{2}\left(x - 3\right)=0

(b)8 marks

Use the factor form to list the distinct real roots in order

\(r_{1}\) \(m_{1}\) \(r_{2}\) \(m_{2}\) \(r_{3}\) \(m_{3}\) \(r_{4}\) \(m_{4}\)