1026 Words5 Pages

Quadratic Equations:
Introduction:
Quadratic equation is a polynomial equation of the 2nd degree. The word ‘quadratic’ comes from the Latin word quadratus which represent the word ‘square’. Quadratic equation is an equation which can be written in the form of ax2 + bx + c = 0, where a and b are coefficients of x2 and x respectively and c is a constant. The coefficient of x2 cannot be zero and the expression ax2 + bx + c is called as ‘quadratic expression’. For example, 4x2 + 5x + 2 = 0 is a quadratic equation while 5x + 2 is not a quadratic equation To find the roots of the equation we’ve to use the formula, (-b±√(b^2-4ac))/2a Sum of the root = -b/a and Product of the root = c/a, where a, b & c are real numbers.
Nature of the roots: A quadratic equation has*…show more content…*

if the speed of the slow train is 30 km/h less than that of the fast train, then what are the speed of the two trains (in km/h)? 90, 60 b) 80, 50 c) 70, 40 d) 60, 70 Answer: Let the speed of the faster train = x km/h and The speed of the slower train = (x – 30) km/h Time taken by the faster train ~ time taken by the slower train = 5 hours i.e., 900/(x-30)- 900/x=5 ⇒ x(x – 30) = 5400 x2 – 30x – 5400 = 0 ⇒ (x + 60)(x – 90) = 0 Either x = -60 or x = 90, x cannot be negative Thus, the speeds are 90 km/h and 60 km/h So, the answer is (a) Find the maximum value of 3 – 6x – 8x2 and the corresponding value of x, if x be real. 33/8, 3/8 b) -33/8, 3/8 c) -33/8, -3/8 d) 33/8, -3/8 Answer: Let us take y = 3 – 6x – 8x2 ⇒ 8x2 + 6x + y – 3 = 0 If x is real, then the discriminant b2 – 4ac ≥ 0 i.e., 62 – 4*8*(y – 3) ≥

if the speed of the slow train is 30 km/h less than that of the fast train, then what are the speed of the two trains (in km/h)? 90, 60 b) 80, 50 c) 70, 40 d) 60, 70 Answer: Let the speed of the faster train = x km/h and The speed of the slower train = (x – 30) km/h Time taken by the faster train ~ time taken by the slower train = 5 hours i.e., 900/(x-30)- 900/x=5 ⇒ x(x – 30) = 5400 x2 – 30x – 5400 = 0 ⇒ (x + 60)(x – 90) = 0 Either x = -60 or x = 90, x cannot be negative Thus, the speeds are 90 km/h and 60 km/h So, the answer is (a) Find the maximum value of 3 – 6x – 8x2 and the corresponding value of x, if x be real. 33/8, 3/8 b) -33/8, 3/8 c) -33/8, -3/8 d) 33/8, -3/8 Answer: Let us take y = 3 – 6x – 8x2 ⇒ 8x2 + 6x + y – 3 = 0 If x is real, then the discriminant b2 – 4ac ≥ 0 i.e., 62 – 4*8*(y – 3) ≥

Related

## How Does Foreign Aid Affect Economic Growth

1574 Words | 7 Pages. “The impact of foreign debt on the economic growth of Pakistan Research problem: The problem of this proposal is to distinguish between the negative and positive impacts of foreign aid. I highlighted the relationship between the two variables impact of foreign aid and economic growth. I want to analyze that whether is it positive or negative? I want to analyze that the increment in foreign aid affects our imports and exports gap and also the saving investment gap either negatively

## Brain Cancer Segmentation Case Study

5655 Words | 23 Pages1 OBJECTIVE AND PROBLEM STATEMENT 1.1 Objective To implement Brain Tumour Segmentation based on Local Independent Projection-based Classification. In which Local independent projection based classification consider data distribution of different classes by learning Softmax regression model which improve classification performance. 1.2 Problem Statement Brain tumour segmentation is an important procedure for early tumour diagnosis and radiotherapy planning. Although numerous brain tumour segmentation

### How Does Foreign Aid Affect Economic Growth

1574 Words | 7 Pages### Brain Cancer Segmentation Case Study

5655 Words | 23 Pages