Question

Find the sum and the product of the roots of the following equations.
$x^2-6x+5$

• A. $6,5$
• B. $6,-5$
• C. $-6,5$
• D. None of these

Answer 1

The correct option is A $6,5$

$\Rightarrow$ The given quadratic equation is $x^2-6x+5=0$, comparing it with $a{x}^2+bx+c=0$

$\therefore$ $a=1,b=-6$ and $c=5$

$\Rightarrow$ Let $\alpha$ and $\beta$ are two roots of given equation.

$\Rightarrow$ $\alpha +\beta =-\frac{b}{a}$

$=-\frac{(-6)}{1}$

$=6$

$\therefore$ $\alpha +\beta =6$

$\Rightarrow$ $\alpha .\beta =\frac{c}{a}$

$=\frac{5}{1}$

$\therefore$ $\alpha .\beta =5$

$\Rightarrow$ The sum and the product of the roots are $6$ and $5$