Question 7: What makes a problem quadratic?Īnswer: It describes a problem that deals with a variable multiplied by itself, which we know as squaring. Furthermore, we can use the quadratic formula to identify the axis f symmetry of the parabola, and the number of real zeros the quadratic equation contains. Question 6: What is the quadratic formula and what is it used for?Īnswer: It refers to a formula that produces the zeros of any parabola. In addition, the standard form of a quadratic equation is y = ax2 + bx + c, where a, b, and c are number and a is not equal to zero (a ≠ 0). This means that the highest exponent of the function is 2.
Speed can’t be negative, so we have x = 6 km/h.Īnswer: We can define this equation as an equation of second degree or degree of 2. Hence, using the quadratic formula, we have x = 6 and x = -54. Simplification of the above equation gives: x 2 + 48x -324 = 0. Therefore, the speed of the motorboat upstream is (18 – x) km/h and the speed of the motorboat downstream is (18 + x) km/h. The speed of the stream is:Ī) 6 km/h B) 5 km/h C) 3.5 km/h D) 4.5 km/hĪnswer : A) Let the speed of the stream be represented by x. Question 4: A motorboat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. The time cannot be negative so, the time = 5 seconds. In other words, when the height is maximum, t = 2 therefore, maximum height = 144m. Hence, for t = 2, the negative term vanishes and we get a maximum value for h. Now for h to be maximum, the negative term should be minimum. Therefore, we have:Ģ) To find the maximum height, let us rearrange the equation: Solution: 1) The given equation is h = -16t 2 + 64t + 80. The time it will take before hitting the ground? The maximum height reached by the ball?ģ. The height reached by the ball after 1 second?Ģ. The height of the ball from the ground at time t is h, and is given by h = -16t 2 + 64t + 80. It will reach a maximum vertical height and then fall back to the ground. Hence, x = 3 and therefore, Area = 1/2 x 3 x 4 = 6ĭownload NCERT Solutions for Class 10 Mathematics Application to Problems of MotionĮxample 3: A ball is thrown upwards from a rooftop, 80 m above the ground. We can only take x = 3 here because the length can’t be negative. X 2 + (x+1) 2 = 5 2 (Pythagoras’ Theorem) Solution: The longest side will be the Hypotenuse. Find x and the area, if the longest side is 5. Therefore, the width is 3 m and length is 5(3) = 15 m.Įxample 2: The three sides of a right-angled triangle are x, x+1 and 5. Then we see that w (5w) will give the area of the hall. Solution: Let us suppose that ‘w’ is the width of the hall. Let us start.īrowse more Topics under Quadratic EquationsĮxample 1: There is a hall whose length is five times the width.
Here we will try to describe a few uses by considering a few examples.
In other fields, we see quadratic equations in many forms. It helps develop a different field of mathematics known as the Complex Analysis. This case, as you will see in later classes is of prime importance. As already discussed, a quadratic equation has no real solutions if D < 0. In mathematics, the solution of the quadratic equation is of particular importance. Many physical and mathematical problems are in the form of quadratic equations.
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