Question

The roots of the quadratic equation $3x^2+2x-1=0$ are $\frac{1}{3}$ and _____.

• A. -1
• B. -2
• C. 1
• D. 2

Answer 1

The correct option is A -1

Consider the quadratic equation $3x^2+2x-1=0.$
Comparing the given quadratic equation with the standard form $a{x}^2+bx+c=0,$ where $a,b$ and $c$ are constants ($a\ne 0$), we have
$a=3,b=2$ and $c=-1.$
Consider the product of $a$ and $c.$
$a\times c=3\times -1=-3$
Factorise $a\times c$ such the numbers add up to $b.$
$\therefore b=2=3+(-1).$
We now simplify the given equation.
Hence, the quadratic equation can be written as
$3x^2+3x-x-1=0.$
$\Rightarrow 3x(x+1)-1(x+1)=0$
$\Rightarrow (3x-1)(x+1)=0$
Now, $(3x-1)=0\Rightarrow x=\frac{1}{3}.$
Also, $(x+1)=0\Rightarrow x=-1$
$\therefore x=\frac{1}{3}$ and $x=-1$ are the roots of the equation.