Quadratic Equations

Hong Kong

Stage 4 - Stage 5

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

4min

We want to solve the following equation for $x$`x`: $25x^4-65x^2+36=0$25`x`4−65`x`2+36=0.

Easy

7min

Consider the equation $81x^4-117x^2+36=0$81`x`4−117`x`2+36=0.

Easy

5min

Consider the equation $\left(4x+8\right)^2+16\left(4x+8\right)+48=0$(4`x`+8)2+16(4`x`+8)+48=0.

Easy

3min

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