Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-2)

Theory of Equation and Inequations

Total Questions: 50

1. If the roots of a quadratic equation a𝓍²+b𝓍+6=0 are -3 and -2, then the value of 'b' is [DSE TGT 2022]

Correct Answer: (d) 5
Solution:

2. If the ratio of roots of an equation 𝓍² - p𝓍 + q = 0 is 1:2, then the relation between p and q is [DSSSB PGT 2021]

Correct Answer: (b) 2p² = 9q
Solution:

3. If 4 be the root of the equation 𝓍²+ a𝓍 - 12 = 0, then another root is [DSSSB PGT 2021]

Correct Answer: (c) -3
Solution:

4. If b = c = 0 in the equation a𝓍² + b𝓍 + c = 0, then the value of roots are

Correct Answer: (c) 0,0
Solution:

5. What is the nature of the roots of this equation 𝓍² - 2√7𝓍 - 2 = 0? [DSSSB PGT 2021]

Correct Answer: (a) Real, Unequal, Irrational
Solution:

6. If a, b and c are real and rational and satisfies the condition a + b + c = 0, of the equation a𝓍² +b𝓍 + c = 0, then the roots are [DSSSB PGT 2021]

Correct Answer: (a) Rational, Real
Solution:

7. The roots of the equation a𝓍² + b𝓍 + c = 0 being equal and having opposite signs can be possible only when [DSSSB PGT 2021 ]

Correct Answer: (b) b = 0
Solution:

8. What is the addition of two roots of the equation 3𝓍²- 5𝓍 + 7 = 0? [DSSSB PGT 2021]

Correct Answer: (c) 5/3
Solution:

3𝓍²- 5𝓍 + 7 = 0
⇒ Sum of roots = 5/3

9. Which of the following equations is having the roots 2 and (-3)? [DSSSB PGT 2021]

Correct Answer: (a) 𝓍² + 𝓍 - 6 = 0
Solution:

If 2 & -3 are roots, then equation
𝓍²-(2-3)𝓍+(2)(-3) =0
𝓍²+𝓍-6 = 0

10. If the subtraction of two roots is 2, of the equation 2𝓍² - 12𝓍 + m + 2 = 0, then the value of m is [DSSSB PGT 2021]

Correct Answer: (c) m = 14
Solution: