Quadratic Equations

NZ Level 7 (NZC) Level 2 (NCEA)

Logs and power functions reducible to quadratics

Consider the equation

$\left(2^x\right)^2-9\times2^x+8=0$(2`x`)2−9×2`x`+8=0

a

The equation can be reduced to a quadratic equation by using a certain substitution.

By filling in the gaps, determine the correct substitution that would reduce the equation to a quadratic.

Let $m=\left(\editable{}\right)^{\editable{}}$`m`=()

b

Solve the equation for $x$`x` by using the substitution $m=2^x$`m`=2`x`.

Easy

Approx 3 minutes

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Manipulate rational, exponential, and logarithmic algebraic expressions

Apply algebraic methods in solving problems