Solve the following Equations

[shaoen01]

Hi,

I need some help with these equations, i don't know what approach i should use to solve them.

1.
\(\displaystyle 3x^{3} + 4x^{2} - 49x + 30 = 0\)

2.
\(\displaystyle 4^{x+1} - 3(2^{3+x}) + 35 = 3(2^{2-1})\)

 

[wjm11]

Hello, Shaoen,

What methods have you learned for solving problems like these?

On the first problem, you could try factoring or graphing. Since it is a 3rd degree polynomial function, you can expect 3 solutions. Solutions might include both real and complex numbers. (In this case, you'll get three real number solutions.)

Graphically, the solutions would be the three places the curve crosses the x-axis.

 

[stapel]

For the second one, I'd suggest simplifying first. For instance, 4^x+1 = (4^x)(4¹) = 4(4^x) = 4((2²)^x) = 4(2^2x) = 4((2^x)²).

Once you're done simplifying everything, you would be able to rearrange the equation into a quadratic in 2^x.

Eliz.