Trying to find the right answer to this..

Here, a = k, b = 4, c = 1 ∴ D = b 2 – 4ac = (4) 2 – 4k x 1 = 16 – 4k Roots are equal and real, if D = 0 ⇒ 16 – 4k = 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.

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?

Here, a = k, b = 4, c = 1
∴ D = b² – 4ac = (4)² – 4k x 1 = 16 – 4k
Roots are equal and real, if D = 0
⇒ 16 – 4k = 0
⇒ k = 4

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.

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78. If one of the roots of the quadratic 2x² + px – 4 = 0 is 4. Write value of p.

164 Views

Short Answer Type

79. Find the discriminant of the quadratic equation.

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80. Show that x = – 3 is a solution of x² + 6x + 9 = 0.

121 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

Long Answer Type

Short Answer Type

Long Answer Type

Short Answer Type

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