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Determine for value of a if sqrt2 is a r...

Determine for value of a if `sqrt2` is a root of the quadratic equation `ax^(2)+sqrt2ax+a=0`.

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The correct Answer is:
a=0
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CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.2
  1. The quadratic equation in one variable x^(2)+1=0 have no roots.

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  2. The roots of the quadratic equation x^(2)+a=0 are .

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  3. The roots of the quadratic equation x^(2)-2x+1=0 are and .

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  4. Solve : sqrtx+(1)/(sqrtx)=2.

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  5. Determine for value of a if sqrt2 is a root of the quadratic equation ...

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  6. Prove that p and q are two roots of the quadratic x^(2)-(p+q)x+pq=0.

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  7. Solve : x+(k)/(x)=sqrt2.

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  8. If (2)/(5)and-5 be two roots of the quadratic equation ax^(2)-5x+b=0, ...

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  9. If sqrt2and-1 be two roots of the quadratic equation sqrt2ax^(2)+bx+1=...

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  10. Solve the equations : x^(2)+2bx-b^(2)=a^(2)-b(b-2x)

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  11. Solve the equations : (b-ax)/(bx-a)=(d-cx)/(dx-c)

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  12. Solve the equations : (1)/(a-b){a^(2)(x-b)-b^(2)(x-a)}=x^(2)

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  13. Solve the equations : (x-3)/(x+3)-(x+3)/(x-3)+6(6)/(7)=0

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  14. Solve the equation abs(x-abs(4-x))-2x=4

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  15. Solve the equations : (x-3)/(x+3)+(x+3)/(x-3)=(2(x+4))/(x-4)

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  16. Solve the equations : ((a-x)/(x+a))^(2)-5((x-a)/(x+a))+6=0

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  17. Solve the equations : ((x+1)^(3)-(x-1)^(3))/((x+1)^(2)-(x-1)^(2))=2

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  18. Solve the equations : (x-a)/(x-b)+(x-b)/(x-a)=(a)/(b)+(b)/(a)

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  19. Solve the equations : (1)/(a+b-x)=(1)/(a)+(1)/(b)-(1)/(x)

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  20. Solve the equations : (x-2)(x-3)-(a+1)/(a^(2))=0

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