Question

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

Answer 1

`18x^2 - 9 x- 5=0\\</p><p>`

Explanation:

Let x be the variable of the required quadratic equation.

`\because - (1)/(3) \: \& \: (5)/(6)` are the roots of the required quadratic equation.

`\therefore \bigg(x+ (1)/(3)\bigg ) \: \& \: \bigg(x-(5)/(6)\bigg)` are factors of the required quadratic equation.

`\therefore \bigg(x+ (1)/(3)\bigg ) \bigg(x-(5)/(6)\bigg) = 0\\\\</p><p>x^2 +\bigg((1)/(3)-(5)/(6)\bigg )x+ \bigg((1)/(3)\bigg )\bigg(-(5)/(6)\bigg )=0\\\\</p><p>x^2 +\bigg((6)/(18)-(15)/(18)\bigg )x- (5)/(18)=0\\\\</p><p>x^2 +\bigg(-(9)/(18)\bigg )x- (5)/(18)=0\\\\</p><p>x^2 - (9)/(18) x- (5)/(18)=0\\\\</p><p>\huge\purple {\boxed {18x^2 - 9 x- 5=0}} \\</p><p>`

is the required quadratic equation