Full solution

Q. Solve the quadratic equation:

(2x^2-5x+3=0)

Identify Coefficients: Identify the coefficients of the quadratic equation $2x^2 - 5x + 3 = 0$ . Compare the given equation with the standard form $ax^2 + bx + c = 0$ to find the coefficients $a$ , $b$ , and $c$ . Here, $a = 2$ , $b = -5$ , and $c = 3$ .
Use Quadratic Formula: Use the quadratic formula to find the roots of the equation. $\newline$ The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ Substitute the values of $a$ , $b$ , and $c$ into the formula. $\newline$ $x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4\cdot 2\cdot 3}}{2\cdot 2}$ .
Simplify Terms: Simplify the terms inside the square root and outside. $\newline$ Calculate the discriminant $b^2 - 4ac$ . $\newline$ Discriminant = $(-5)^2 - 4\cdot 2\cdot 3 = 25 - 24 = 1$ . $\newline$ Now, the formula becomes $x = \frac{5 \pm \sqrt{1}}{4}$ .
Calculate Roots: Calculate the roots using the simplified quadratic formula. $\newline$ Since the discriminant is positive, we will have two real roots. $\newline$ Root $1$ : $x = \frac{5 + \sqrt{1}}{4} = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$ . $\newline$ Root $2$ : $x = \frac{5 - \sqrt{1}}{4} = \frac{5 - 1}{4} = \frac{4}{4} = 1$ .