Quadratic Equations

Hong Kong

Stage 4 - Stage 5

Given that $ax^2-15x+25=\left(2x-5\right)\left(x-5\right)$`a``x`2−15`x`+25=(2`x`−5)(`x`−5) for all values of $x$`x`, solve for $a$`a`.

Easy

1min

Given that $3x^2+4x-2$3`x`2+4`x`−2$\equiv$≡$a\left(x-3\right)^2+b\left(x-3\right)+c$`a`(`x`−3)2+`b`(`x`−3)+`c` for all real $x$`x`, answer the following.

Easy

7min

Given that $x^2+6x+14=a\left(x+b\right)^2+c$`x`2+6`x`+14=`a`(`x`+`b`)2+`c` for all real values of $x$`x`, answer the following.

Easy

3min

Consider the identity $a\left(x-4\right)+b\left(7-x\right)=3x-4$`a`(`x`−4)+`b`(7−`x`)=3`x`−4.

Easy

5min

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