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Quadratic Equations

Short Answer Type

81. Show that x = – 3 is a solution of 2x² + 5x – 3 = 0.

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82. Show that x = – 2 is a solution of 3x² + 13x + 14 = 0.

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83. What is the descriminant of the following equation:
2x² – 3x + 1 = 0

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84. Find the values of K for which the given equation Kx² – 6x – 2 = 0 has real roots.

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85. Find the values of K for which the equation x² + 5Kx + 16 = 0 has no real roots.

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86. Write the values of k for which the quadratic equation x² – kx + 9 = 0 has equal roots.

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87. What is the nature of roots of the quadratic equation 4x² – 12x – 9 = 0?

Here, a = 4, b = –12 and c = –9
D = b² – 4ac
= (–12)² – 4 (4) (–9)
= 144 + 144 = 288
Since D > 0, therefore, roots of the given equation are real and unequal. Ans.

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88. Is x = –2 a solution of the equation x² – 2x + 8 = 0?

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89. Write the nature of roots of quadratic equation

4 straight x squared plus 4 square root of 3 straight x plus 3 equals 0.

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90. Represent the following situation in the form of quadratic equation and find solutions.
The sum of two numbers is 18 and their product is 45.

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Previous Year Papers

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Short Answer Type

87. What is the nature of roots of the quadratic equation 4x2 – 12x – 9 = 0?

87. What is the nature of roots of the quadratic equation 4x² – 12x – 9 = 0?