quadratic equation @ jpjzhf9的部落格

標題:

quadratic equation

發問:

1.A graph of y=3x^2+7x+p where p＞0.Find all the possible integral value(s) of p. 2.A graph of y=-x^2+3k+k.It cuts the x-axis at two pointsA(-1,0) and B,and cuts the y-axis at point C. (a)Find the value of k. (b)Find the coordinates of B and C. (c)Find the area of traingle ABC 更新: 1.delta has 2 distinct real roots

最佳解答:

1) product of root = p / 3 Since p > 0, p / 3 > 0 The root is negative-negative or positive-positive of positive delta = 49 - 12p >= 0 12p <= 49 p <= 49/12 So, the possible integral value are 1, 2, 3, 4. 圖片參考：http://imgcld.yimg.com/8/n/HA05931286/o/701008250334813873381800.jpg 2a) Since the quadratic equation cuts the x-axis at 2 points, Put (-1 , 0) into equation, 0 = -1 - 3 + k k = 4, b) y = -x^2 + 3x + 4 x^2 - 3x - 4 = 0 (x - 4)(x + 1) = 0 x = 4 or -1 So, the coordinates of B is (4,0) C cuts the y-axis, put x = 0, y = 0 + 0 + 4 = 4 So, the coordinates of C is (0,4) c) distance of AB = 4 - (-1) = 5 distance of OC = 4 Area of ABC = 5 * 4 * 1/2 = 10 sq. units

其他解答:

Sorry that I make a mistake.