Find the roots of the quadratic equation $2x^2 - 5x + 3 = 0$ by using the quadratic formula.

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Accepted Answer

To find the roots of the given quadratic equation $2x^2 - 5x + 3 = 0$ using the quadratic formula, follow these step-by-step calculations: Step 1: Compare the given equation with the standard form of a quadratic equation, which is $ax^2 + bx + c = 0$.
From the comparison, we get: $a = 2$ $b = -5$ $c = 3$ Step 2: Write down the quadratic formula for finding the roots of $x$: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$| Step 3: Calculate the discriminant ($D = b^2 - 4ac$) first to check the nature of the roots: $$D = (-5)^2 - 4(2)(3)$$ $$D = 25 - 24$$ $$D = 1$$
Since $D > 0$, the equation has two distinct real roots. Step 4: Substitute the values of $a$, $b$, and $D$ into the quadratic formula: $$x = \frac{-(-5) \pm \sqrt{1}}{2(2)}$$ $$x = \frac{5 \pm 1}{4}$| Step 5: Split the $\pm$ sign to find the two individual values of $x$:
For the positive sign (+): $$x1 = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$$ 
For the negative sign (-): $$x2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$$ Final Answer: 
The roots of the given quadratic equation are $x = \frac{3}{2}$ and $x = 1$.

MP Board · Class 10 · Mathematics · Quadratic EquationsFind the roots of the quadratic equation $2x^2 - 5x + 3 = 0$ by using the quadratic formula.