Question

How to find quadratic equations from -1/3 and 5/6

Answer 1

Answer:

$18x^2 - 9 x- 5=0\\

$

Step-by-step explanation:

Let x be the variable of the required quadratic equation.

$\because - \frac{1}{3} \: \& \: \frac{5}{6}$ are the roots of the required quadratic equation.

$\therefore \bigg(x+ \frac{1}{3}\bigg ) \: \& \: \bigg(x-\frac{5}{6}\bigg)$ are factors of the required quadratic equation.

$\therefore \bigg(x+ \frac{1}{3}\bigg ) \bigg(x-\frac{5}{6}\bigg) = 0\\\\

x^2 +\bigg(\frac{1}{3}-\frac{5}{6}\bigg )x+ \bigg(\frac{1}{3}\bigg )\bigg(-\frac{5}{6}\bigg )=0\\\\

x^2 +\bigg(\frac{6}{18}-\frac{15}{18}\bigg )x- \frac{5}{18}=0\\\\

x^2 +\bigg(-\frac{9}{18}\bigg )x- \frac{5}{18}=0\\\\

x^2 - \frac{9}{18} x- \frac{5}{18}=0\\\\

\huge\purple {\boxed {18x^2 - 9 x- 5=0}} \\

$

is the required quadratic equation