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Quadratic Equations

Short Answer Type

71. Find the discriminant of the following quadratic equations, and hence find the nature of its roots.

negative straight x squared plus 2 straight x plus 3 equals 0

109 Views

72. Find the discriminant of the following quadratic equations, and hence find the nature of its roots.

straight x squared plus straight x plus 1 equals 0

92 Views

73. For what value of A, are the roots of the quadratic equation 3x² + 2kx + 27 = 0 real and equal?

The given quadratic equation is
3x² + 2kx + 27 = 0
Here, a = 3, b = 2k and c = 27
D = b² – 4ac = (2k²) – 4 x 3 x 27 = 4k² – 324
The given equation will have real and equal roots, if
$straight D equals 0 space rightwards double arrow space 4 straight k squared minus 324 equals 0 space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space 4 straight k squared space equals 324$
$rightwards double arrow straight k squared space equals space 81 space rightwards double arrow space straight k space equals plus-or-minus square root of 81 space equals space plus-or-minus 9 space space Ans. space$

547 Views

74. For what value of A, are the roots of the quadratic equation: kx² + 4x + 1 = 0 equal and real?

224 Views

Long Answer Type

75. For what value of A, does (k – 12)x² + 2 (k – 12)x + 2 = 0 have equal roots?

375 Views

Short Answer Type

76. For what value of A, does the equation 9x² + 3kx + 4 = 0 have equal roots?

626 Views

Long Answer Type

77. If (–5) is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, then find the values of p and A.

117 Views