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The smallest value of k, for which both ...

The smallest value of k, for which both the roots of the equation, `x^2-8kx + 16(k^2-k + 1)=0` are real, distinct and have values at least 4, is

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VIKAS GUPTA (BLACK BOOK)-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of negative intergral values of m for which the expression ...

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

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  3. The smallest value of k, for which both the roots of the equation, x^2...

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

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

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

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

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

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  9. Let p (x) be a polynomial equation of least possible degree, with rati...

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  10. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

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  11. Let p (x) be a polynomial with real coefficient and p (x)=p'(x) =x^(2)...

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  12. Find the smallest positive integral value of a for which the greater r...

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  13. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

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  14. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

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  15. The number of integral value of a,a, in [-5, 5] for which the equation...

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  16. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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  17. Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x...

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  18. If x and y are real numbers connected by the equation 9x ^(2)+2xy+y^(2...

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  19. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

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  20. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

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