Without solving, examine the nature of the roots of the equation $2 x^{2} - 6 x + 3 = 0$ .

Open in App

Solution

Finding the nature of roots of the equation $2 x^{2} - 6 x + 3 = 0$ .
Compare the given quadratic equation $2 x^{2} - 6 x + 3 = 0$ with the standard quadratic equation $a x^{2} + b x + c = 0$ .
$\begin{array}{rcl} a & = & 2 \\ b & = & - 6 \\ c & = & 3 \end{array}$
The discriminant of the quadratic equation is,
$D = b^{2} - 4 a c$
Determine the value of $D$ .
$\begin{array}{rcl} D & = & {(- 6)}^{2} - 4 \times 2 \times 3 \\ = & 36 - 24 \\ = & 12 > 0 \end{array}$
Since, $D > 0$ , the equation has two real and distinct roots.
Thus, the quadratic equation $2 x^{2} - 6 x + 3 = 0$ has two real and distinct roots.

Suggest Corrections

Similar questions

Without solving, examine the nature of roots of the equations 2 $x^{2}$ – 5x + 5 = 0

Without solving, examine the nature of the roots of the equation:

$3 x^{2} + 2 x - 1 = 0$

Without solving, examine the nature of roots of the equation.

4 $x^{2}$ – 4x + 1 = 0 [2 MARKS]

Without solving examine the nature of the roots of the equation:

$4 x^{2} + 3 x - 1 = 0$

Without solving , examine the nature of roots of the following quadratic equations:

(i) $25 x^{2} - 10 x + 1 = 0$

(ii) $2 x^{2} + 8 x + 9 = 0$

Join BYJU'S Learning Program