Question

What are the roots of the quadratic equation? 6x2+5x−4=0 12 and −113 −12 and −113 −12 and 113 12 and 113

Answer 1

Answer:

The roots of the quadratic equation are:

       $x=\dfrac{1}{2}\ and\ x=\dfrac{-4}{3}$

Step-by-step explanation:

Any quadratic equation of the type:

    $ax^2+bx+c=0$

has solutions as:

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

Here we have quadratic equation as:

$6x^2+5x-4=0$

i.e.

$a=6\ ,\  b=5\ and\ c=-4$

Hence, the solution is given by:

$x=\dfrac{-5\pm \sqrt{5^2-4\times 6\times (-4)}}{2\times 6}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{25+96}}{12}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{121}}{12}\\\\i.e.\\\\x=\dfrac{-5\pm 11}{12}\\\\x=\dfrac{-5+11}{12}\ and\ x=\dfrac{-5-11}{12}\\\\x=\dfrac{6}{12}\ and\ x=\dfrac{-16}{12}\\\\x=\dfrac{1}{2}\ and\ x=\dfrac{-4}{3}$