AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

61. The relationship between the roots and coefficients of a quadratic equation \( ax^2 + bx + c = 0 \) is given by:

• a) \( x_1 + x_2 = \frac{-b}{a} \), \( x_1x_2 = \frac{c}{a} \)
• b) \( x_1 + x_2 = \frac{b}{a} \), \( x_1x_2 = \frac{c}{a} \)
• c) \( x_1 + x_2 = \frac{a}{b} \), \( x_1x_2 = \frac{b}{c} \)
• d) \( x_1 + x_2 = \frac{c}{b} \), \( x_1x_2 = \frac{a}{c} \)

Answer: a) \( x_1 + x_2 = \frac{-b}{a} \), \( x_1x_2 = \frac{c}{a} \)

62. If the equation \( x^2 - 6x + 9 = 0 \) has roots \( r_1 \) and \( r_2 \), then the sum and product of the roots are:

• a) \( r_1 + r_2 = -6 \), \( r_1r_2 = 9 \)
• b) \( r_1 + r_2 = 6 \), \( r_1r_2 = 9 \)
• c) \( r_1 + r_2 = 9 \), \( r_1r_2 = 6 \)
• d) \( r_1 + r_2 = 6 \), \( r_1r_2 = 6 \)

Answer: b) \( r_1 + r_2 = 6 \), \( r_1r_2 = 9 \)

63. If the roots of the equation \( x^2 - 3x + 2 = 0 \) are \( 1 \) and \( 2 \), then the sum of the roots is:

• a) 3
• b) 1
• c) 2
• d) 4

Answer: a) 3

64. In an equation with real coefficients, if one root is complex, then the other root is:

• a) Real
• b) Imaginary
• c) Complex conjugate
• d) Zero

Answer: c) Complex conjugate

65. If two roots of a cubic equation are \( 2 \) and \( 3 \), and the third root is the sum of these two roots, the equation is:

• a) \( x^3 - 5x^2 + 6x = 0 \)
• b) \( x^3 - 5x^2 + 11x - 6 = 0 \)
• c) \( x^3 + 5x^2 + 6x = 0 \)
• d) \( x^3 - 6x^2 + 5x = 0 \)

Answer: b) \( x^3 - 5x^2 + 11x - 6 = 0 \)

66. The equation whose roots are the reciprocals of the roots of \( ax^2 + bx + c = 0 \) is:

• a) \( cx^2 + bx + a = 0 \)
• b) \( ax^2 + cx + b = 0 \)
• c) \( ax^2 - bx + c = 0 \)
• d) \( ax^2 + bx + c = 0 \)

Answer: a) \( cx^2 + bx + a = 0 \)

67. In an equation \( x^2 + px + q = 0 \), if the roots are \( \alpha \) and \( \beta \), the sum of the roots is:

• a) \( p \)
• b) \( -p \)
• c) \( q \)
• d) \( -q \)

Answer: b) \( -p \)

68. If the equation \( x^2 - 5x + 6 = 0 \) has roots \( r_1 \) and \( r_2 \), then the equation with roots \( \frac{1}{r_1} \) and \( \frac{1}{r_2} \) is:

• a) \( x^2 - 5x + 6 = 0 \)
• b) \( x^2 - 6x + 5 = 0 \)
• c) \( x^2 - 6x + 6 = 0 \)
• d) \( x^2 - 5x + 5 = 0 \)

Answer: b) \( x^2 - 6x + 5 = 0 \)

69. The equation \( x^2 + px + q = 0 \) has roots \( \alpha \) and \( \beta \). The equation whose roots are \( \alpha + \beta \) and \( \alpha \beta \) is:

• a) \( x^2 + px + q = 0 \)
• b) \( x^2 - px + q = 0 \)
• c) \( x^2 - qx + p = 0 \)
• d) \( x^2 + qx - p = 0 \)

Answer: c) \( x^2 - qx + p = 0 \)

70. If the equation \( ax^2 + bx + c = 0 \) has real roots, the discriminant must be:

• a) Positive
• b) Zero
• c) Negative
• d) Any real number

Answer: a) Positive