Question

2.Solve the following quadratic equations
i. 9x^2 - 1/16
ii. 2h^2 - 3h - 27

Answer 1

`i)~9x^2-(1)/(16)=0\iff9x^2=(1)/(16)\iff x^2=(1)/(9\cdot16)\iff \\\\x^2=(1)/(144)\iff x=\pm\sqrt{(1)/(144)}=\pm(1)/(12)\Longrightarrow\boxed{x=\pm(1)/(12)}`



`ii)~2h^2-3h-27=0\\\\\Delta=b^2-4ac\to \Delta=(-3)^2-4\cdot2\cdot(-27)\to\Delta=9+216=225\\\\ \Longrightarrow h=(-b\pm√(\Delta))/(2a)=(-(-3)\pm√(225))/(2\cdot2)=(3\pm15)/(4)\\\\\begin{cases}h_1=(3+15)/(4)=(18)/(4)\iff \boxed{h_1=(9)/(2)}\\h_2=(3-15)/(4)=(-12)/(4)\iff\boxed{h_2=-3}\end{cases}`