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Polynomials Test - 45

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Polynomials Test - 45
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  • Question 1
    1 / -0
    Write the correct alternative answer for the following question .
    Which of the following is a polynomial .
    Solution

  • Question 2
    1 / -0
    Find all the zeros of the polynomial x43x310x2+36x24x^4-3x^3-10x^2+36x-24, if 12\sqrt{12} and 12-\sqrt{12} are two of its zeros.
    Solution

  • Question 3
    1 / -0
    Find the sum of zeroes of the polynomial 2x4+x314x219x62x^4+x^3-14x^2-19x-6, if two of its zeroes are 1-1 and 33
    Solution

  • Question 4
    1 / -0
    If the two zeros of the polynomial  x285x+c=0{ x }^{ 2 }-85x+c=0 are prime numbers, what is the value of the sum of the digits of c?
  • Question 5
    1 / -0
    Consider the cubic equation x3(1+cosθ +sinθ)x2+(cosθsinθ +cosθ +sinθ)xsinθcosgq=0,{x^3} - \left( {1 + \cos \theta  + \sin \theta } \right){x^2} + \left( {\cos \theta \sin \theta  + \cos \theta  + \sin \theta } \right)x - \sin \theta \cos gq = 0, whose roots are x1,x2  and  x3.{x_1},{x_2}\,\,{\text{and}}\,\,{x_3}. 
    1. The value of x12+x22+x32x_1^2 + x_2^2 + x_3^2 equals
  • Question 6
    1 / -0
    If α,beta\alpha,beta are zeros of polynomial f(x)=2x2+5x+kf(x)=2x^2+5x+k satisfying the relation α2+β2+αβ=214\alpha^2+\beta^2+\alpha\beta=\cfrac{21}{4} then K=
    Solution

  • Question 7
    1 / -0
    State whether the given algebraic expressions are polynomials ?
  • Question 8
    1 / -0
    If α\alpha,β\beta are zero of quadratic polynomial kx2+6x+6\displaystyle kx^2 + 6x + 6 , then find the value of k such that (α+β)22αβ=24 \displaystyle ( \alpha + \beta )^2 2\alpha \beta = 24
  • Question 9
    1 / -0
    If the zeroes of the polynomial f(x) =x39kx2+52kx24k3{ x }^{ 3 }-{ 9kx }^{ 2 }+52kx-24{ k }^{ 3 } are in the ratio 2:3:4, then the possible value of k is 
  • Question 10
    1 / -0
    If α\alpha and β\beta are zeros of the quadratic polynomial f(x)=ax2+bx+cf(x)=ax^2+bx+c, then βaα+b+αaβ+b=\frac {\beta}{a\alpha +b}+\frac {\alpha }{a\beta +b}=
    Solution

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