Question

1. 3a^3 - 14a^2 - 5a =0



2. 8x + 4 =0


3. y^2 + 9y + 14 =0

Answer 1

the first one factorize in a(3a^2-14a-5)=0

now from here we have...

a=0 or 3a^2-14a-5=0

to solve 3a^2-14a-5=0 you have the quadratic equation... use

\[\Large x_{1/2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] and you'll have two solutions

\[\Large a_1=-\frac13 \quad a_2=5 \quad a_3=0 \quad(\text{a_3 we have taken from principal})\]


the second task is easier...

8x+4=0

8x=-4

\[\Large x=-\frac{4}{8} \Longrightarrow x=-\frac12\]

now regarding question nr. 3 is similar as part two of the first question ... use quadratic formula and you'll have....

\[\LARGE y_1=-7 \quad \quad y_2=-2\]