Question

find the roots of the quadratic equation 2 x square - 5 x minus 3 is equal to zero by using formula method​

Answer 1

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Answer 2

The roots of the quadratic equation are: $\quad x=3,\:x=-\frac{1}{2}$

Step-by-step explanation:

Consider the provided quadratic equation.

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

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are:

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

Substitute $a=2,\:b=-5,\:c=-3$ in above.

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

$x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{25+24}}{2\cdot \:2}$

$x_{1,\:2}=\frac{5\pm \sqrt{49}}{4}$

$x_{1,\:2}=\frac{5\pm 7}{4}$

$x_{1}=\frac{5+7}{4}\ or\ x_{2}=\frac{5-7}{4}\\\\x_{1}=\frac{12}{4}\ or\ x_{2}=\frac{-2}{4}\\\\x_{1}=4\ or\ x_{2}=-\frac{1}{2}$

Hence, the roots of the quadratic equation are: $\quad x=3,\:x=-\frac{1}{2}$

#Learn more

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