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If alpha and beta are the ral roots of x...

If `alpha and beta` are the ral roots of `x ^(2) + px +q =0 and alpha ^(4), beta ^(4) ` are the roots of `x ^(2) - rx+s =0.` Then the equation `x ^(2) -4qx+2q ^(2)-r =0` has always `(alpha ne beta, p ne 0 , p,q, r, s in R)`:

A

one positive and one negative root

B

two positive roots

C

two negative roots

D

can't say anything

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Verified by Experts

The correct Answer is:
A
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VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

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  11. The number of all values of n, (whre n is a whole number ) for which t...

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  12. The number of negative intergral values of m for which the expression ...

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  13. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

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  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

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  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  18. Find the number of integral vaues of 'a' for which the range of functi...

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  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

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