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Method and examples
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Method
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1. If `alpha` and `beta` are roots of quadratic equation `2x^2-3x-6=0`, then find `alpha^2+beta^2`
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If `alpha,beta` are roots of ,
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then find the value of
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- `3x^2+8x+2=0`, find `a^2+b^2`
- `3x^2+8x+2=0`, find `a-b`
- `3x^2+8x+2=0`, find `a^3+b^3`
- `3x^2+8x+2=0`, find `a/b^2+b/a^2`
- `3x^2+8x+2=0`, find `ab^2+ba^2`
- `3x^2+8x+2=0`, find `a/b+b/a`
- `3x^2+8x+2=0`, find `1/a+1/b`
- `3x^2+8x+2=0`, find `a^2b^2+2a^2+2b^2+4`
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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`
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If `alpha,beta` are roots of ,
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then form the equation whose roots are ,
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- `2x^2+3x-1=0`, find equation whose roots are `a/b,b/a`
- `2x^2+3x-1=0`, find equation whose roots are `a/b^2,b/a^2`
- `2x^2+3x-1=0`, find equation whose roots are `a^2+2,b^2+2`
- `2x^2+3x-1=0`, find equation whose roots are `a+1,b+1`
- `2x^2+3x-1=0`, find equation whose roots are `a^2b,b^2a`
- `2x^2+3x-1=0`, find equation whose roots are `2a+3b,3a+2b`
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3. Find value of `k` for which quadratic equation `2x^2+kx+2=0` has real roots
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Find value of k for which
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has
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- `x^2-kx-4=0`, has real roots
- `2x^2+kx+2=0`, has real roots
- `x^2+4mx+4m^2+m+1=0`, has real roots
- `2x^2+kx+2=0`, has equal roots
- `x^2+2(k+2)x+9k=0`, has equal roots
- `mx^2+2x+m=0`, has distinct roots
- `3x^2+11x+k=0`, has reciprocal roots
- `(k+1)x^2-5x+3k=0`, has reciprocal roots
- `(k^2+1)x^2-13x+4k=0`, has reciprocal roots
- `x^2+kx+2=0`, has sum of roots = -3
- `x^2+3x+k=0`, has product of roots = 2
- `x^2-(k+6)x+2(2k-1)=0`, has sum of roots = `1/2` product of roots
- `kx^2+2x+3k=0`, has sum of roots = product of roots
- `x^2+kx+8=0`, has `a-b=2`
- `x^2+6x+k=0`, has `a-b=2`
- `x^2-6x+k=0`, has `3a+2b=20`
- `px^2-14x+8=0`, has `a=6b`
- `2x^2+kx+2=0`, has one root 2
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Solution
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Solution provided by AtoZmath.com
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If alpha and beta are roots of quadratic equation, then find `alpha^2+beta^2`
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3. Find value of `k` for which
 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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