Method and examples
Method  

1. Discriminant and nature of roots of quadratic equation
 
Equation =
Find 
  1. `25x^2-30x+9=0`
  2. `2x^2+5x-10=0`
  3. `x^2+10x-56=0`
  4. `4x^2+11x+10=0`
  5. `x^2-2x=8`
  6. `x^2-25=0`
  7. `x^2+5x+3=0`
  8. `9x^2-24x+16=0`

2. Find the quadratic equation whose roots are alpha and beta
Alpha (α) =
Beta (β) =
  1. `3,-4`
  2. `-1/2,+2/3`
  3. `2,-2/3`
  4. `3sqrt(7),-3sqrt(7)`
  5. `sqrt(7),-sqrt(7)`
  6. `1+3sqrt(2),1-3sqrt(2)`
  7. `(3+5sqrt(3))/2,(3-5sqrt(3))/2`
  8. `(-3+5sqrt(3))/2,(-3-5sqrt(3))/2`
  9. `(-3+sqrt(3))/2,(-3-sqrt(3))/2`

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