Reduce the quadratic form qf= xरिड्यूस द क्वालिटी फॉर्म ऑफ यू एस 2X 1x टू प्लस टू एक्स प्लस 3 प्लस टू एक्स एक्स एक्स 1 * यू कैन नॉट कैनॉनिकल फॉर्म बाय डायगोनल मैट्रिक्स ऑप्टी क्वालिटी फॉर्म एंड अटेनमेंट एंड नेचुरल नेचुरल
Answers
Answer:
Solve the equation: x2 + 3x – 4 = 0
Solution: This method is also known as splitting the middle term method. Here, a = 1, b = 3, c = -4. Let us multiply a and c = 1 * (-4) = -4. Next, the middle term is split into two terms. We do it such that the product of the new coefficients equals the product of a and c.
We have to get 3 here. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. Hence, we write x2 + 3x – 4 = 0 as x2 + 4x – x – 4 = 0. Thus, we can factorise the terms as: (x+4)(x-1) = 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 have either (x+4) = 0 or (x-1) = 0 or both are = 0. This gives x+4 = 0 or x-1 = 0. Solving these equations for x gives: x=-4 or x=1. This method is convenient but is not applicable to every equation. In those cases, we can use the other methods as discussed below.