Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-4)

Theory of Equation and Inequations

Total Questions: 50

41. If the equation 9√𝓍-7√𝓍-36 = -16, then the value of '𝓍' is: [Haryana TGT 2019]

Correct Answer: (d) 100
Solution:

42. If α, β,λ are zeros of the cubic polynomial a𝓍³ +b𝓍² +c𝓍 +d, then αβ+βγ+αγ is equal to: [Haryana TGT 2019]

Correct Answer: (c) c/a
Solution:

43. The zeros of the quadratic polynomial 𝓍² +99𝓍 +127 are: [Haryana TGT 2019]

Correct Answer: (b) Both negative
Solution:

Let α and β be the zeros of the quadratic polynomial 𝓍² + 99𝓍 + 127
Then we have
Sum of zeros = α + β  = -99
&  Product of zeros = αβ = 127
Which clearly shows that both the zeros, α and β, must be negative.

44. If the roots of the equation 3𝓍² + 2𝓍 + p(p - 1) = 0 are of opposite signs, then: [Haryana PGT 2020]

Correct Answer: (b) p ∈ (0,1)
Solution:

Given equation 3𝓍² + 2𝓍 + p(p - 1) = 0
If the roots of the given equation are of opposite sign then product of roots is negative i.e.

45. If 1 is a twice repeated root of the equation a𝓍³ +b𝓍² +b𝓍+d = 0, then: [Haryana PGT 2018]

Correct Answer: (b) a = d = -b
Solution:

46. If α, β are the roots of the equation 𝓍²-𝓍+1 = 0, the equation whose roots are α², β² is : [UKPSC GIC 2018]

Correct Answer: (b) x²+𝓍+1= 0
Solution:

47. If α and β are the roots of the equation 𝓍²- 2𝓍 +4=0, then value of αⁿ+βⁿ is [(GIC) EXAM, 2015]

Correct Answer: (a)
Solution:

48. The roots of the equation 𝓍³- 12𝓍²+ 39𝓍 – 28-0 are in A.P., the common difference is [UP TGT-2016 (08-03-2019)]

Correct Answer: (b) 3
Solution:

49. If 𝓍–1 and 𝓍+3 are the two factors of 𝓍³+ a𝓍 +b, then remaining factor is [UP TGT-2016 (08-03-2019)]

Correct Answer: (b) 𝓍-2
Solution:

50. The equations 2𝓍-ky+7 =0 and 6𝓍-12y+15 = have no solution for [UP TGT-2016 (08-03-2019)]

Correct Answer: (b) k =4
Solution: