Question

Solve the following quadratic equation using the quadratic formula. Which of the following expressions gives the numerators of the solutions?
10x^2 - 19x + 6 = 0

Answer 1

I hope the choices for the numerators of the solutions are given.

I am showing the complete work to find the solutions of this equation , it will help you to find an answer of your question based on this solution.

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

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

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = 10, b = -19 and c = 6.

Next step is to plug in these values in the above formula. Therefore,

$x=\frac{(-19)-\pm\sqrt{(-19)^2-4*10*6}}{2*10}$

$=\frac{19\pm\sqrt{361-240}}{20}$

$=\frac{19\pm\sqrt{121}}{20}$

$=\frac{19\pm11}{20}$

So, $x=\frac{19-11}{20} ,\frac{19+11}{20}$

$x=\frac{8}{20} , \frac{30}{20}$

So, $x= \frac{2}{5} ,\frac{3}{2}$

Hope this helps you!

Answer 2

This is the answer:

19 ± 11