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If cos A, cos B and cos C are the roots of the cubic `x^(3)+ax^(2)+bx+c=0`, where A,B,C are the angles of a triangle, then the value of `a^(2)-2b-2c` is

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VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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

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

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

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

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  6. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

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  7. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

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  8. Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+...

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  9. The number of ordered pairs (a,b) where a,b are integers satisfying th...

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  10. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

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  11. If the range of the values of a for which the roots of the equation x ...

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  12. Find the number of positive integers satisfying the inequality x^(2) -...

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  13. If sin theta and cos theta are the roots of the quadratic equation ax...

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  14. Let the inequality sin ^(2) x+a cos x +a ^(2) ge1+ cos x is satisfied...

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  15. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

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  16. The sum of all integral values of 'a' for which the equation 2x ^(2) -...

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  17. Let f (x) be a polynomial of degree 8 such that F(r)=1/r, r=1,2,3,…,8,...

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  18. Let alpha, beta are two real roots of equation x ^(2) + px+ q =0, p ,q...

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  19. If cos A, cos B and cos C are the roots of the cubic x^(3)+ax^(2)+bx+c...

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  20. Find the value of a for which a x^2+(a-3)x+1<0 for at least one positi...

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