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What are the roots of the equation x^(2)...

What are the roots of the equation `x^(2)+sqrt(2)x-4=0.`

A

`sqrt2` and `-sqrt2`

B

`sqrt2` and `sqrt2`

C

`sqrt2` and `2sqrt2`

D

`sqrt2` and `-2sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
D
The given equation is `x^(2)+sqrt(2)x-4=0.`
Putting `x=sqrt(2)` in the given equation, we get
`LHS=(sqrt(2))^(2)+(sqrt(2)xxsqrt(2))-4=(2+2-4)=0=RHS.`
`:." "sqrt(2)` is a root of the given equation.
Putting `x=-2sqrt(2)` in the given equation, we get
`LHS=(-2sqrt(2))^(2)+sqrt(2)xx(-2sqrt(2))-4=(8-4-4)=0=RHS.`
`:." "-2sqrt(2)` is a root of the given equation.
Hence, `sqrt(2)` and `-2sqrt(2)` are the roots of the given equation.
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RS AGGARWAL-QUADRATIC EQUATIONS -Test Yourself
  1. What are the roots of the equation x^(2)+sqrt(2)x-4=0.

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  2. Which of the following is a quadratic equation?

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  3. Which of the following is a quadratic equation ?

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  4. Which of the following is not a quadratic equation?

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  5. If x=3 is a solution of the equation 3x^(2)+(k-1)x+9=0 then k=?

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  6. If one root of the equation 2x^(2)+ax+6=0 is 2 then a=?

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  7. The sum of the roots of the equation x^(2)-6x+2=0 is

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  8. If the product of the roots of the equation x^(2)-3x+k=10 is -2 then t...

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  9. The ratio of the sum and product of the roots of the equation 7x^(2)-1...

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  10. If one root of the equation 3x^(2)-10x+3=0" is "(1)/(3) then the other...

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  11. If one root of 5x^(2)+13x+k=0 be the reciprocal of the other root then...

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  12. If the sum of the roots of the equation kx^(2)+2x+3k=0 is equal to the...

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  13. The roots of a quadratic equation are 5 and -2. Then, the equation is

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  14. If the sum of the roots of aquadratic equation is 6 and their product...

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  15. If alpha and beta are the roots of the equation 3x^(2)+8x+2=0 then ((1...

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  16. The roots of the equation ax^(2)+bx+c=0 will be reciprocal of each oth...

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  17. If the roots of the equation ax^(2)+bx+c=0 are equal then c=?

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  18. If the equation 9x^(2)+6kx+4=0 has equal roots then k=?

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  19. If the equation x^(2)+2(k+2)x+9k=0 has equal roots then k= ?

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  20. If the equation 4x^(2)-3kx+1=0 has equal roots then k=?

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  21. The roots of ax^(2)+bx+c=0, ane0 are real and unequal, if (b^(2)-4ac)

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