Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-8)

Theory of Equation and Inequations

Total Questions: 33

11. If 𝓍, π“Ž and 𝓏 are real and different, then the equation u= 𝓍² +4π“ŽΒ² +9𝓏² +12π“Žπ“-4𝓏𝓍 -2π“π“Ž is always [TGT 2010]

Correct Answer: (b) non-negative
Solution:

12. If 1 is a root of equation a𝓍²+b𝓍+c=0, then- [TGT 2009]

Correct Answer: (d) a+b+c= 0
Solution:

If 1 is the root of the quadratic equation Β a𝓍²+b𝓍+c=0 then 𝓍 = 1 will satisfy the equation.
a.1Β² +b.1 +c = 0 β‡’ a+b+c = 0

13. If the quadratic equation p𝓍²-2𝓍+2 = 0 has real linear factor, the value of p will be [TGT 2009]

Correct Answer: (a)
Solution:

14. If eˣ = y+√(1+y²), the y = [TGT 2009]

Correct Answer: (b)
Solution:

15. The number of root of the quadratic equation 8secΒ²ΞΈ - 6secΞΈ +1 = 0 will be [TGT 2009]

Correct Answer: (d) 0
Solution:

16. If one root of equation a𝓍² + b𝓍 + c = 0 is square of another root then- [TGT 2009]

Correct Answer: (b) bΒ³+ac (a+c) = 3abc
Solution:


17. If tanΞ± and tanΞ² are roots of quadratic equation 𝓍²- p𝓍 + q = 0. Then the value of sinΒ²(Ξ±+Ξ²) will be; [TGT 2009]

Correct Answer: (a)
Solution:

18. The difference of roots of quadratic equation 𝓍²-6𝓍+6=0 is- [TGT 2005]

Correct Answer: (c) √12
Solution:

19. In a quadratic equation 𝓍²+p𝓍+q = 0, taken coefficient of 𝓍 17 instead of 13 by which obtained roots are –2 & –15. Therefore, what is orginal roots of the equation? [TGT 2005]

Correct Answer: (c) -10, -3
Solution:

20. If 𝓍 is real and K=(𝓍²-x+1)/𝓍²+𝓍+1, then [TGT 2005]

Correct Answer: (a)
Solution: