Find the value of x in the equation 2x^2 + 5x - 3 = 0 using the quadratic formula. Also, explain the significance of the quadratic formula in solving quadratic equations.

Q: Find the value of x in the equation 2x^2 + 5x - 3 = 0 using the quadratic formula. Also, explain the significance of the quadratic formula in solving quadratic equations.

Quadratic Formula \nThe quadratic formula is a mathematical formula that provides the solutions to a quadratic equation of the form ax^2 + bx + c = 0. The quadratic formula is given by: \nx = (-b ± √(b^2 - 4ac)) / 2a \nwhere a, b, and c are the coefficients of the quadratic equation. Significance of the Quadratic Formula \nThe quadratic formula is a powerful tool for solving quadratic equations. It provides a general solution to the equation, which can be used to find the values of x that satisfy the equation. The quadratic formula is also useful for finding the roots of a quadratic equation, which can be used to solve a wide range of problems in mathematics and science. Step-by-Step Solution \nTo find the value of x in the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula. The coefficients of the equation are a = 2, b = 5, and c = -3. Plugging these values into the quadratic formula, we get: \nx = (-5 ± √(5^2 - 4(2)(-3))) / 2(2) \nSimplifying the expression, we get: \nx = (-5 ± √(25 + 24)) / 4 \nx = (-5 ± √49) / 4 \nx = (-5 ± 7) / 4 \nTherefore, the solutions to the equation are x = (-5 + 7) / 4 and x = (-5 - 7) / 4. \nx = 2 / 4 and x = -12 / 4 \nx = 1/2 and x = -3 \nTherefore, the value of x in the equation 2x^2 + 5x - 3 = 0 is x = 1/2 or x = -3.

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Quadratic Formula 
The quadratic formula is a mathematical formula that provides the solutions to a quadratic equation of the form ax^2 + bx + c = 0. The quadratic formula is given by: 
x = (-b ± √(b^2 - 4ac)) / 2a 
where a, b, and c are the coefficients of the quadratic equation. Significance of the Quadratic Formula 
The quadratic formula is a powerful tool for solving quadratic equations. It provides a general solution to the equation, which can be used to find the values of x that satisfy the equation. The quadratic formula is also useful for finding the roots of a quadratic equation, which can be used to solve a wide range of problems in mathematics and science. Step-by-Step Solution 
To find the value of x in the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula. The coefficients of the equation are a = 2, b = 5, and c = -3. Plugging these values into the quadratic formula, we get: 
x = (-5 ± √(5^2 - 4(2)(-3))) / 2(2) 
Simplifying the expression, we get: 
x = (-5 ± √(25 + 24)) / 4 
x = (-5 ± √49) / 4 
x = (-5 ± 7) / 4 
Therefore, the solutions to the equation are x = (-5 + 7) / 4 and x = (-5 - 7) / 4. 
x = 2 / 4 and x = -12 / 4 
x = 1/2 and x = -3 
Therefore, the value of x in the equation 2x^2 + 5x - 3 = 0 is x = 1/2 or x = -3.

MP Board · Class 10 · Mathematics · PolynomialsFind the value of x in the equation 2x^2 + 5x - 3 = 0 using the quadratic formula. Also, explain the significance of the quadratic formula in solving quadratic equations.