Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-3)

Theory of Equation and Inequations

Total Questions: 50

31. Find the discriminant of 6𝓍² +5𝓍 +7 = 0. [OAVS TGT 2017]

Correct Answer: (d) 137
Solution:

Discriminant of quadratic eqn a𝓍²+b𝓍+c = 0 is D= b² - 4ас
Hence, in eqn 6𝓍²+5𝓍+7 = 0,
D= (5)²-4×6×7
⇒ D = 25-168
⇒D = -143

32. |x|<2 equivalent to : [OAVS TGT 2017]

Correct Answer: (d) -2<𝓍<2
Solution:

We know that if |𝓍|<2
⇒ -2 <𝓍< 2 is correct.

33. If 𝓍 - b is a factor of F(𝓍), then which of the following is TRUE? [OAVS TGT 2017]

Correct Answer: (a) F(b) = 0
Solution:

If (𝓍-b) is a factor of F(𝓍), then, 𝓍 = b will satisfy the eqn then, F(b) = 0.

34. 3𝓍²+ 11𝓍 + k = 0 is an equation with reciprocal roots, what is the value of k? [OAVS TGT 2017]

Correct Answer: (d) 3
Solution:

35. If α, β are the roots of the equation 4𝓍²- 5𝓍+3=0, then find α²β + αβ²? [OAVS TGT 2017]

Correct Answer: (a) 15/16
Solution:

36. What are the roots of equation 𝓍³ - 5𝓍²-2𝓍 + 24 = 0? [OAVS TGT 2017]

Correct Answer: (b) -2, 3,4
Solution:

37. Roots of the equation 𝓍² - 9𝓍 + 6 = 0 are: [OAVS TGT 2017]

Correct Answer: (c)
Solution:

38. According to Cauchy-Schwarz, if 𝓍³ + y²+ z² = 1, then what is the maximum value of 𝓍 + 2y + 3z =0? [OAVS TGT 2017]

Correct Answer: (c) √14
Solution:

39. One real root of the equation 𝓍³ + 𝓍 - 2 = 0 is [OAVS TGT 2017]

Correct Answer: (a) 1
Solution:

40. The values of 𝓍 by solving the trinomial 2𝓍² +9𝓍-5 are: [OAVS TGT 2017]

Correct Answer: (d) 1/2, -5
Solution: