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1.10 Solve cubic equations

Lesson

Similar to solving quadratics we have a few methods to choose between when solving cubic equations:

  • Solve using algebraic manipulation - For cubics such as $2x^3+16=0$2x3+16=0.
  • Factorise - Fully factorising the cubic and then we can then use the null factor law to solve. If $a\times b=0$a×b=0 then either $a=0$a=0 or $b=0$b=0.
  • Technology - Once we have extracted the important information from a question and formed an equation, we could use technology to solve the equation graphically or algebraically. 

 

When factorising a cubic recall we can factorise by:

  • using the highest common factor
  • factor special forms such as the sum and difference of cubes
  • identifying a single factor, then using division to establish the remaining quadratic. From here you would employ any of the factorising methods for quadratics.  

 

Practice questions

Question 1

Solve the equation $x^3=-8$x3=8.

QUESTION 2

Solve the equation $x^3-49x=0$x349x=0.

  1. State the solutions on the same line, separated by a comma.

QUESTION 3

The cubic $P\left(x\right)=x^3-2x^2-5x+6$P(x)=x32x25x+6 has a factor of $x-3$x3.

  1. Solve for the roots of the cubic. If there is more than one root, state the solutions on the same line separated by commas.

Outcomes

1.2.4.5

solve cubic equations using technology, and algebraically in cases where a linear factor is easily obtained

1.2.4.7

solve equations involving combinations of the functions above, using technology where appropriate

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