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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?

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.

∵ (–5) is a root of the quadratic equation
∴ 2x² + px – 15 = 0
2(–5)² + p. (–5) – 15 = 0
⇒ 50 – 5p – 15 = 0
⇒ –5p + 35= 0
⇒ –5p = –35
⇒ P = 7
Now. the quadratic equation 7(x² + x) + k = 0
i.e. 7x² + 7x + k = 0 has equal roots.
∴ Its discriminant $straight D equals left parenthesis 7 right parenthesis squared minus 4 cross times 7 cross times straight k space is space zero$
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$rightwards double arrow$ $straight k equals 49 over 28 equals 7 over 4$

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