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The values of the parameter a for which ...

The values of the parameter a for which the quadratic equations `(1 – 2a) x^2 – 6ax – 1 = 0` and `ax^2 – x+1 = 0` have at least one root in common are

A

`(1)/(2), (2)/(9)`

B

`0, (1)/(2)`

C

`(2)/(9)`

D

`0, (1)/(2), (2)/(9)`

Text Solution

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The correct Answer is:
C
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ARIHANT SSC-THEORY OF EQUATIONS-EXERCISE(LEVEL 1)
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  3. The values of the parameter a for which the quadratic equations (1 – 2...

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  4. The integer k for which the inequality x^2 - 2 (4k -1) x+ 15 k^...

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  6. The condition that x^(3)-ax^(2)+bx-c=0 may have two of its roots equal...

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  7. If the roots of ax^(2) + bx + c = 0 (a gt 0) be each greater than unit...

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  8. The number of real solutions of x-1/(x^2-4)=2-1/(x^2-4) is equal to

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  9. The number of real solutions of equation 2^(x/2)+(sqrt2+1)^x=(5+2sqrt2...

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  10. If x y=2(x+y),xlt=ya n dx ,y in N , then the number of solutions of t...

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  11. The quadratic equation ax^(2)+bx+c=0 has real roots if:

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  12. The equation |x+1||x-1|=a^(2) - 2a - 3 can have real solutions for x, ...

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  13. p, q, r in R and k is a prime number such that p+qk^(1//3)+rk^(2//3)=0...

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  15. For a<0, deterine all real roots of the equation x^2-2a|x-a|-3a^2=0.

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  18. If a, b in {1, 2, 3, 4}, then the number of quadratic equations of the...

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  19. The minimum value of the expression a+(1)/(a), a gt0 is :

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  20. If a^2+b^2+c^2=1 then ab+bc+ca lies in the interval

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