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Let p, q be integers and let `alpha , beta ` be the roots of the equations `x^(2) - x - 1 = 0 " where " alpha ne beta`. For n = 0,1,2, . . . let `a_(n) = palpha ^(n) +q beta^(n)` . If `a_(4) = 28` , then p ` +(1)/(8) q` is equal to ______

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`4 . 50`
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MCGROW HILL PUBLICATION-QUADRATIC EQUATIONS-Exercise ( Level 2 (Numerical answer type questions))
  1. Let alpha , beta be non-real roots of (x^(2) + x - 3) (x^(2) + x - 2) ...

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  2. Suppose alpha, beta are irrational roots of x^(5) - 5x^(4) + 9x^(3) +...

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  3. Suppose alpha, beta, gamma are roots of x^(3) + qx + r = 0 . If (al...

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  4. Suppose f(x) = (x - a) (x - b) - (1)/(2) (b - a), where a b in R . If ...

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  5. Let f(x) = (x^(2) + 4x + 1)/( x^(2) + x + 1), x inR If m le f(x) l...

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  6. If a, b gt 0, then the least value of (a^(2) - ab + b^(2))/((a + b)^(2...

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  7. Let p, q be integers and let alpha , beta be the roots of the equatio...

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  8. Let alpha , beta be roots of x^(2) + x +1 = 0, then the equation whos...

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  9. Let S = {x in R : sqrt(x^(2) + 19 x ) - sqrt(x) + sqrt(x + 19) = x + 6...

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  10. Suppose a, b in Q and 3 - sqrt(5) is a root of x^(2) + ax + b = 0 , "t...

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  11. If y = x + (1)/(x) , (x ne 0) reduces the polynomial (x^(2) -5x + 1) (...

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  12. Suppose, a, b, c in R, a gt 0. Let alpha , beta be roots of ax^(2) + b...

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  13. If the equations x^(5) + ax + 1= 0 and x^(6) + ax^(2) + 1= 0 have a c...

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  14. If 3 + 4i is a root of x^(2) + px + q = 0, where p, q in R , then (1)/...

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  15. Suppose p ne q and difference between the roots of x^(2) + 2px + q = 0...

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  16. If the equation formed by decreasing each root of ax^(2) + bx + c = 0"...

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  17. Suppose a, b, c in R, a ne 0 .If one root of ax^(2) + bx + c = 0 is th...

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  18. Let a, b be roots of x^(2) + 2x + 5 . 71 = 0. "Let" A(n) be alpha^(n) ...

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  19. Let f(x) = (x^(2) + x + 1)/(x^(2) + 3 x + 3) x x in R . Let m be the m...

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