Question

5.72 +237 +12The roots of the function are18 and - 4The roots of the function are (52 - 4) (2-3)O The factored form is (5x + 2) (0 + 10)The factored form is (5x + 2) (x+6)

Answer 1

Determine the factored form of the equation by splitting the middle term.

$\begin{gathered} 5x^2+23x+12=5x^2+20x+3x+12 \\ =5x(x+4)+3(x+4) \\ =(x+4)(5x+3) \end{gathered}$

So factored form of equation is (x + 4)(5x + 3).

Determine the roots of the equation by equating the equation to 0.

$\begin{gathered} 5x^2+23x+12=0 \\ (x+4)(5x+3)=0 \\ x+4=0\text{ or 5x + 3 = 0} \\ x\text{ =-4 or x = -3/5} \\ x=-4,-\frac{3}{5} \end{gathered}$

So roots of the equation are -4 and -3/5.