Algebra I help: Solving Quadratics with the Zero Product

[Carbunkel]

Using Zero Product, how would you solve a problem such as "4x^2+5x+1=0" or something like "5(x+7)^2." I've been looking through my notes to solve said equations; however, to no avail.

Comments will be greatly appreciated, thanks.

 

[galactus]

Factor:

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This should be in any algebra book.

\(\displaystyle \L\\4x^{2}+5x+1=0\)

What 2 numbers when added equal 5 and when multiplied equal 4.

That's right, 4 and 1.

\(\displaystyle \L\\4x^{2}+4x+x+1\)

\(\displaystyle \L\\4x(x+1)+(x+1)\)

Factor:

\(\displaystyle \L\\(4x+1)(x+1)=0\)

Now, what makes this equal 0?. Try \(\displaystyle \frac{-1}{4}, \;\ -1\)

 

[Denis]

Using Zero Product, how would you solve a problem such as "4x^2+5x+1=0" or something like "5(x+7)^2."

5(x + 7)^2 is NOT an equation :shock: