Quadratic Equation
 Which of the following equations is a quadratic ?

 x^{3}  x^{2}  x + 5 = 0
 x^{4}  10
 7x^{2} = 49
 x^{4}  x^{3} = 9000
 None of the above

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Quadratic equation must be in the form of ax^{2} + bx + c = 0, where a ≠ 0.
Correct Option: C
Clearly, 7x^{2} = 49 or 7x^{2}  49 = 0, which is of the form ax^{2} + bx + c = 0, where b = 0.
Thus, 7x^{2}  49 = 0 is a quadratic equation.
 Which of the following equations has real roots ?

 2x^{2}  3x + 4 = 0
 (x  1) (2x  5) = 0
 3x^{2} + 4x + 5 = 0
 Cannot be determined
 None of the above

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(x  1) (2x  5) = 0 ⇒ x = 1, 5/2
So, its roots are real.Correct Option: B
(x  1) (2x  5) = 0 ⇒ x = 1, 5/2
So, its roots are real.
 Find the roots of the equation 2x^{2}  9x  18 = 0.

 3/2 and 6
 3/2 and  6
 3/2 and 6
 3/2 and 6
 None of the above

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Given equation is 2x^{2}  9x  18 = 0
[by factorisation method]
⇒ 2x^{2}  12x + 3x  18 = 0Correct Option: C
Given equation is 2x^{2}  9x  18 = 0
[by factorisation method]
⇒ 2x^{2}  12x + 3x  18 = 0
⇒ 2x(x  6) + 3(x  6) = 0
⇒ (2x + 3) (x  6) = 0
∴ x = 3/2, 6
 If one root of x^{2}  6kx + 5 = 0 is 5, find the value of k.

 1/2
 1
 1
 2

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Given, one root of x^{2}  6kx + 5 = 0 is 5.
∴ x = 5 satisfies x^{2}  6kx + 5 = 0Correct Option: C
Given, one root of x^{2}  6kx + 5 = 0 is 5.
∴ x = 5 satisfies x^{2}  6kx + 5 = 0
⇒ 5^{2}  30k + 5 = 0
⇒ 25  30k + 5 = 0
⇒ 30  30k = 0
⇒ 30k = 30
∴ k = 1
 Find the roots of the equation 2x^{2}  11x + 15 = 0

 3 and 5/2
 3 and 5/2
 5 and 3/2
 5 and 3/2

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2x^{2} 11x + 15 = 0
[by factorisation method]
⇒ 2x^{2}  (6x + 5x) + 15 = 0Correct Option: A
2x^{2} 11x + 15 = 0
[by factorisation method]
⇒ 2x^{2}  (6x + 5x) + 15 = 0
⇒ 2x^{2}  6x  5x + 15 = 0
⇒ 2x(x  3)  5 (x  3) = 0
⇒ (2x  5) (x  3) = 0
∴ x = 5/2, 3
Hence, the roots are 5/2 and 3.