QUADRATIC EQUATIONS AND INEQUATIONS (CDS)

Total Questions: 67

61. In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was [2014 (I) Morning Shift]

Correct Answer: (c) x² - 10x + 9 = 0
Solution:When mistake is done in first degree term, then the roots of the equation are -9 and -1.

62. If m and n are the roots of the equation 27ax² + bx + c = 0, then the equation whose roots are (m² + 1) / m and (n² + 1) / n is [2014 (I) Morning Shift]

Correct Answer: (a) acx² + (ab + bc)x + b² + (a - c)² = 0
Solution:For the given equation ax² + bx + c = 0, m and n are the roots.


63. The value of x² - 4x + 11 can never be less than [2014 (I) Morning Shift]

Correct Answer: (a) 7
Solution:Let f (x) = x² - 4x + 11

64. The expression 2x³ + x² - 2x - 1 is divisible by [2014 (I) Morning Shift]

Correct Answer: (b) 2x + 1
Solution:

65. If x + y = 5 , y + z = 10 and z + x = 15 then which one of the following is correct? [2014 (I) Morning Shift]

Correct Answer: (a) z > x > y
Solution:Given equations

66. If the roots of the equation (a² - bc) x² + 2(b² - ac) x + (c² - ab) = 0 are equal, where b ≠ 0 , then which one of the following is correct? [2014 (I) Morning Shift]

Correct Answer: (d) a³ + b³ + c³ = 3abc
Solution:Given equation is (a² - bc) x² + 2(b² - ac) x + (c² - ab) = 0

67. If the roots of the equation Ax² + Bx + C = 0 are -1 and 1, then which one of the following is correct? [2014 (I) Morning Shift]

Correct Answer: (d) A and Care of opposite signs
Solution:Given equation is Ax² + Bx + C = 0  ...(i)