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Quadratic Equation Determining an Unknown When Roots are given
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Quadratic Equation: Determining an Unknown When its Root(s) are Given
A quadratic equation is an equation with unknown variable to the second power.
The standard form of a quadratic equation is ax2 + bx + c = 0, (a 0)
Where a, b, and c are constants and x is the unknown variable.
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Solutions of Problems Involving Quadratic Equations
Example: If x = 2 and x = 3 are roots of the equation 3x - 2lx + 2n =0, find the values of l and n.
Solution: Since x = 2 and x = 3 are roots of the equation 3x2 - 2lx + 2n = 0
3 * 22 - 2l * 2 + 2n=0 and 3 * 32 - 2l * 3 + 2n = 0
       12 = 4l + 2n = 0 and 27 = 6l - 2n = 0
       12 = 4l + 2n and 27 = 6l - 2n
Solving these two equations, you get
l = 15/2 and n = 9

Example: If one root of the quadratic equation 2x2 + nx - 6 = 0 is 2, find the value of n. Also, find the other root.
Solution: Since x = 2 is a root of the equation
2x2 + nx - 6 = 0.
      2 * 22 + 2n - 6 = 0
      8 + 2n - 6 = 0
      2n + 2 = 0 
      n = -1.
Substituting n = -1 in the equation 2x2 + nx - 6 = 0, you get
2x2 - x - 6 = 0 2x2 - 4x + 3x - 6 = 0
     2x (x - 2) + 3(x - 2) = 0
     (x - 2) (2x + 3) = 0 
      x - 2 = 0, 2x + 3 = 0
     x = 2, and x - 3/2
Hence, the other roots is -3/2.
 
   
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