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If q(t)=4t^(3)+4t^(2)-t-1andq(-1/2)=0, t...

If `q(t)=4t^(3)+4t^(2)-t-1andq(-1/2)=0`, then determine the polynomial by which q(t) is divisible.

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.3
  1. If the polynomial p(x)=x^(3)+3x^(2)+3x+1 be divided by (x-pi), the rem...

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  2. Determine the remainder when (x^(2)-2pix+pi) is divided by (x-2pi).

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  3. If q(t)=4t^(3)+4t^(2)-t-1andq(-1/2)=0, then determine the polynomial ...

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  4. Find the value of k if p(x)=x^(2)+kx+6andp(2)=0.

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  5. Find the remainder if f(x)=x^(3)+4x^(2)+4x-3 is divided by x.

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  6. Determine the value of c if one of the roots of the equation of the po...

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  7. If f(x)=x^(2)-4x+14, g(x) = x - 1, q(x) = x - 3 and f(x) = g(x) q(x) +...

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  8. Find the roots of the equation of the polynomial p(x) = cx + d.

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  9. Determine the roots of the equation of the polynomial f(x,y)=x^(2)-y^(...

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  10. If the polynomial p(x)=x^(4)-a^(2)x^(2)+2x-a be divisible by (x + a), ...

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  11. If f(x) = (x - 7) q(x) + r(x), where f(x)=x^(3)-7x^(2)+1 and r(x) = 1,...

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  12. What is the vital difference between identity and equation ?

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  13. What is meant by the root of an equation ? Find the root of the equati...

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  14. State and prove Remainder theorem.

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  15. Find the value of k when one of the roots of the equation of the polyn...

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  16. If the roots of the equation x^(3)+ax^(2)-bx-6=0 be -1 and 2, calculat...

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  17. If the roots of the equation of the polynomial f(x)=x^(3)+ax+b be -2 a...

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  18. If the root of the equation of the polynomial p(x)=8x^(3)-px^(2)-4x+2 ...

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  19. If the polynomial f(x)=2x^(3)+ax^(2)+bx-2 be divided by (2x - 3) and (...

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  20. If the polynomial p(x)=4x^(3)-px^(2)+x-q be divided by (x - 1) and (x ...

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