Trying to find the right answer to this..

Here a = 9, b = 3k, c = 4 ∴ D = b 2 – 4ac = (3k) 2 – 4 x 9 x 4 = 9k 2 – 144 Roots are equal, if D = 0 ⇒ 9k 2 – 144 = 0 ⇒ 9k 2 = 144 ⇒ 9k 2 – 144 = 0 ⇒ k 2 – 16 = 0 ⇒ (k) 2 – (4) 2 = 0 ⇒ (k + 4) (k – 4) = 0 ⇒ k + 4 = 0 or, k – 4 = 0 ⇒ k = 4

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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

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

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

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

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Long Answer Type

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

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Short Answer Type

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

Here a = 9, b = 3k, c = 4
∴ D = b² – 4ac = (3k)² – 4 x 9 x 4 = 9k²– 144
Roots are equal, if D = 0
⇒ 9k² – 144 = 0
⇒ 9k² = 144
⇒ 9k² – 144 = 0
⇒ k²– 16 = 0
⇒ (k)² – (4)²= 0
⇒ (k + 4) (k – 4) = 0
⇒ k + 4 = 0 or, k – 4 = 0
⇒ k = 4

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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.

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