Question

determinr the nature roots of qud. equation
3x²-5x-2=0​

Answer 1

Answer:

$3x^2-5x-2=0$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$a=3,\:b=-5,\:c=-2:\quad x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:3\left(-2\right)}}{2\cdot \:3}$

$=\frac{-\left(-5\right)+\sqrt{\left(-5\right)^2-4\cdot \:3\left(-2\right)}}{2\cdot \:3}:\quad 2$

$=\frac{-\left(-5\right)-\sqrt{\left(-5\right)^2-4\cdot \:3\left(-2\right)}}{2\cdot \:3}:\quad -\frac{1}{3}$

$x_{1} =2,\:x_{2} =-\frac{1}{3}$