Parabola y = 3x & # 178; - X-2 the tangent equation of the intersection of parabola and x-axis is solved by means of Weida theorem

Parabola y = 3x & # 178; - X-2 the tangent equation of the intersection of parabola and x-axis is solved by means of Weida theorem

Let y = 3x ^ 2-x-2 = 0
The solution is XA = - 2 / 3, XB = 1
Then the intersection of parabola and X axis is a (- 2 / 3,0) and B (1,0)
(1) Let the tangent passing through point a be y = KX + B
The simultaneous equation can be obtained as 3x ^ 2-x-2 = KX + B
The result is: 3x ^ 2 - (1 + k) x - (B + 2) = 0
Then, according to Weida's theorem, it can be concluded that:
x1+x2=xA+xA=(-2/3)+(-2/3)=-4/3=(k+1)/3
The solution is: k = - 5
x1*x2=xA*xA=(-2/3)^2=4/9=-(b+2)/3
The solution is: B = - 10 / 3
Therefore, the tangent equation of point a is y = - 5x-10 / 3
(2) Let the tangent through point B be y = MX + n
The simultaneous equations give 3x ^ 2-x-2 = MX + n
The result is: 3x ^ 2 - (1 + m) x - (n + 2) = 0
Then, according to Weida's theorem, it can be concluded that:
x1'+x2'=xB+xB=1+1=(m+1)/3
The solution is m = 5
x1*x2=xB*xB=1*1=1=-(n+2)/3
The solution is: n = - 5
Therefore, the tangent equation of point B is y = - 5x-5