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Question 5: What is the formula for solving quadratic equation?Īnswer: The general quadratic equation formula is “ax 2 + bx + c”. Hence, from the quadratic formula, we have: Question 4: Find the value of x: 27 x 2 − 12 = 0Ī) 2/3 B) ± 2/3 C) Ambiguous D) None of theseĪnswer : B) Here, a = 27, b = 0 and c = -12.
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Therefore, x = − 1 More Solved Examples For You The below image illustrates the best use of a quadratic equation.ĭiscriminant = b 2 − 4ac = 22 − 4×1×1 = 0 The quantity in the square root is called the discriminant or D. Just plug in the values of a, b and c, and do the calculations. We define it as follows: If ax 2 + bx + c = 0 is a quadratic equation, then the value of x is given by the following formula: This is the general quadratic equation formula. A method that will work for every quadratic equation. For such equations, a more powerful method is required. There are equations that can’t be reduced using the above two methods. This is known as the method of completing the squares.
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Thus we have either (x+4) = 0 or (x-1) = 0 or both are = 0. For any two quantities a and b, if a×b = 0, we must have either a = 0, b = 0 or a = b = 0. Thus, we can factorise the terms as: (x+4)(x-1) = 0. Hence, we write x 2 + 3x – 4 = 0 as x 2 + 4x – x – 4 = 0. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. We do it such that the product of the new coefficients equals the product of a and c. Next, the middle term is split into two terms. Solution: This method is also known as splitting the middle term method. Examples of FactorizationĮxample 1: Solve the equation: x 2 + 3x – 4 = 0 Let’s see an example and we will get to know more about it. Hence, from these equations, we get the value of x. These factors, if done correctly will give two linear equations in x. Certain quadratic equations can be factorised. The first and simplest method of solving quadratic equations is the factorization method.