Question

If $x$ and $y$ are the roots of the equation $4k^2+5k+6=0$, then match the following with their values.

• A. $-\frac{5}{4}$
• B. $\frac{3}{2}$
• C. $-\frac{5}{6}$

Answer 1

For a quadratic equation given by $a{x}^2+bx+c$ = 0,
the sum of the roots $=-\frac{b}{a}$,
the product of the roots $=\frac{c}{a}$.
Given quadratic equation: $4k^2+5k+6=0$,
Here, $a=4,b=5,c=6$

Here, $x+y=$ sum of the roots $=-\frac{5}{4}$.
Here, xy $=$ product of the roots $=\frac{6}{4}$$=\frac{3}{2}$.
Also, $\frac{1}{x}+\frac{1}{y}=\frac{y+x}{xy}=\frac{Sumoftheroots}{Productoftheroots}$
$=-\frac{5}{6}$.