Question

find zeros of polynomial
4x^2+5√2-12​

Answer 1

Answer:

$roots\\\dfrac{3}{2\sqrt{2}}\\and\\-2\sqrt{2}$

Step-by-step explanation:

pre-requisite knowledge

$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

question $4x^2+5\sqrt{2}-12=0$

$a=4\\b=5\sqrt{2}\\c=-12\\\dfrac{-b\:\pm\:\sqrt{b^2-4ac}}{2a}\\\dfrac{-5\sqrt{2}\pm\sqrt{25*2-4*(-12)(4)}}{2*4}\\\implies\:\dfrac{-5\sqrt{2}\pm\sqrt{242}}{8}\\let's factorise 242\\\begin{array}{c|c}2&242\\\cline{2-2}11&121\\\cline{2-2}11&11\\\cline{2-2}&1\end{array}\\\implies\:\dfrac{-5\sqrt{2}\pm11\sqrt{2}}{8}\\\implies\:\dfrac{\sqrt{2}(-5+11)}{4\sqrt{2}\sqrt{2} }}\\\implies\:\dfrac{6}{4\sqrt{2}}\:\implies\:\dfrac{3}{2\sqrt{2}}\\similarly\\\dfrac{-5\sqrt{2}-11\sqrt{2}}{8}$$\implies\:\dfrac{-16\sqrt{2}}{8}\\\implies\:-2\sqrt{2}$