Question

The roots of the quadratic equation $2x^2-5x+3=0$ are .

• A. 1 and 6
• B. 1 and $\frac{3}{2}$
• C. 1 and $\frac{2}{3}$

Answer 1

The correct option is B 1 and $\frac{3}{2}$

Given equation is $2x^2-5x+3=0.$
Standard form of a quadratic equation is $a{x}^2+bx+c=0$
On comparing with the standard form, $a=2,b=-5$ and $c=3.$
Find the factor pair of $a\times c$ such that the numbers add up to $b.$
$a\times c=6$
Factor pairs of 6 are $1\times 6,2\times 3,-1\times -6,-2\times -3$
Let's consider numbers -2 and -3.
$(-3)\times (-2)=6=a\times c$
$(-3)+(-2)=-5=b$
We now simplify the given equation,
$2x^2-5x+3=0.$
$\Rightarrow 2x^2-2x-3x+3=0$
$\Rightarrow 2x(x-1)-3(x-1)=0$
$\Rightarrow (x-1)(2x-3)=0$
$\Rightarrow x=1$ and $x=\frac{3}{2}$
$\therefore$ 1 and $\frac{3}{2}$ are the roots of the given equation.