Quadratic Equations

NZ Level 7 (NZC) Level 2 (NCEA)

Variable substitution method

We want to solve the following equation for $x$`x`: $x^4-34x^2+225=0$`x`4−34`x`2+225=0.

a

What substitution can we make to reduce this equation to a quadratic in the variable $p$`p`?

b

Substitute $p=x^2$`p`=`x`2 into the equation and solve for $p$`p`.

c

Now solve for $x$`x` using your previous answer as a reference. Write all solutions on the same line, separated by a comma.

Easy

Approx 4 minutes

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Manipulate rational, exponential, and logarithmic algebraic expressions

Apply algebraic methods in solving problems