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

Theory of Equation and Inequations

Total Questions: 33

1. If the roots of the equation 𝓍³-12𝓍²+39𝓍-28 = 0 are in A.P. then the common difference of A.P. will be: [TGT 2003, 2013]

Correct Answer: (d) 3
Solution:

2. If (2+i) is a root of equation 𝓍²- a𝓍+1=0. Then the value of a is [TGT 2013]

Correct Answer: (b) 4
Solution:

3. The graph of a linear equation in two variable will be: [TGT 2013]

Correct Answer: (b) Equation of line
Solution:

Linear equations in two variables are always lines. If there is a quadratic equation in two variables, then it can be a circle, a parabola, an ellipse or a hyperbola.

4. Solve the following equation? [UP PCS (Pre) 1997, PGT 2013]

Correct Answer: (a) k
Solution:

5. The equation f(𝓍) = 𝓍³-𝓍²-8𝓍+12 = 0 has double root α, then α is a root of: [UP PCS (Pre) 1997, PGT 2013]

Correct Answer: (b) f(𝓍)=0
Solution:


6. The roots of the equation 𝓍³+p𝓍² +q𝓍+r=0 are α, β and γ. The value of αβ+βγ+ γα is: [UP PCS (Pre) 1997]

Correct Answer: (b) q
Solution:

7. ∑a² (b-c) is equal to [TGT 2010]

Correct Answer: (c) a² (b-c) +b² (c-a) +c² (a-b)
Solution:

8. If the roots of equation 2𝓍²+k𝓍-8 = 0 are equal and of opposite sign, then the value of k is. [TGT 2010]

Correct Answer: (a) 0
Solution:

9. If the sum of two roots of equation. [TGT 2010]

𝓍³-5𝓍²-16𝓍+80 = 0 be zero, then all the roots are

Correct Answer: (a) 4,-4, 5
Solution:

10. Solve the following equation? [TGT 2010]

Correct Answer: (c) bcx²+(b²+ac)𝓍+ab = 0
Solution: