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Home > Algebra calculators > Find value of `k` for which quadratic equation has real roots calculator
Method and examples
Method  
1. If `alpha` and `beta` are roots of quadratic equation `2x^2-3x-6=0`, then find `alpha^2+beta^2`
If `alpha,beta` are roots of ,
then find the value of
 
  1. `3x^2+8x+2=0`, find `a^2+b^2`
  2. `3x^2+8x+2=0`, find `a-b`
  3. `3x^2+8x+2=0`, find `a^3+b^3`
  4. `3x^2+8x+2=0`, find `a/b^2+b/a^2`
  5. `3x^2+8x+2=0`, find `ab^2+ba^2`
  6. `3x^2+8x+2=0`, find `a/b+b/a`
  7. `3x^2+8x+2=0`, find `1/a+1/b`
  8. `3x^2+8x+2=0`, find `a^2b^2+2a^2+2b^2+4`
2. If `alpha` and `beta` are roots of quadratic equation `2x^2-3x-6=0`, then find equation whose roots are `alpha^2` and `beta^2`
If `alpha,beta` are roots of ,
then form the equation whose roots are ,
 
 
  1. `2x^2+3x-1=0`, find equation whose roots are `a/b,b/a`
  2. `2x^2+3x-1=0`, find equation whose roots are `a/b^2,b/a^2`
  3. `2x^2+3x-1=0`, find equation whose roots are `a^2+2,b^2+2`
  4. `2x^2+3x-1=0`, find equation whose roots are `a+1,b+1`
  5. `2x^2+3x-1=0`, find equation whose roots are `a^2b,b^2a`
  6. `2x^2+3x-1=0`, find equation whose roots are `2a+3b,3a+2b`
3. Find value of `k` for which quadratic equation `2x^2+kx+2=0` has real roots
Find value of k for which
has
 
  1. `x^2-kx-4=0`, has real roots
  2. `2x^2+kx+2=0`, has real roots
  3. `x^2+4mx+4m^2+m+1=0`, has real roots
  4. `2x^2+kx+2=0`, has equal roots
  5. `x^2+2(k+2)x+9k=0`, has equal roots
  6. `mx^2+2x+m=0`, has distinct roots
  7. `3x^2+11x+k=0`, has reciprocal roots
  8. `(k+1)x^2-5x+3k=0`, has reciprocal roots
  9. `(k^2+1)x^2-13x+4k=0`, has reciprocal roots
  10. `x^2+kx+2=0`, has sum of roots = -3
  11. `x^2+3x+k=0`, has product of roots = 2
  12. `x^2-(k+6)x+2(2k-1)=0`, has sum of roots = `1/2` product of roots
  13. `kx^2+2x+3k=0`, has sum of roots = product of roots
  14. `x^2+kx+8=0`, has `a-b=2`
  15. `x^2+6x+k=0`, has `a-b=2`
  16. `x^2-6x+k=0`, has `3a+2b=20`
  17. `px^2-14x+8=0`, has `a=6b`
  18. `2x^2+kx+2=0`, has one root 2
 


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