## Quadratic Equation

#### Quadratic Equation

1. Which of the following equations is a quadratic ?
1. x3 - x2 - x + 5 = 0
2. x4 - 10
3. 7x2 = 49
4. x4 - x3 = 9000
5. None of the above

1. Quadratic equation must be in the form of ax2 + bx + c = 0, where a ≠ 0.

##### Correct Option: C

Clearly, 7x2 = 49 or 7x2 - 49 = 0, which is of the form ax2 + bx + c = 0, where b = 0.
Thus, 7x2 - 49 = 0 is a quadratic equation.

1. Which of the following equations has real roots ?
1. 2x2 - 3x + 4 = 0
2. (x - 1) (2x - 5) = 0
3. 3x2 + 4x + 5 = 0
4. Cannot be determined
5. None of the above

1. (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.

1. Find the roots of the equation 2x2 - 9x - 18 = 0.
1. 3/2 and 6
2. -3/2 and - 6
3. -3/2 and 6
4. 3/2 and -6
5. None of the above

1. Given equation is 2x2 - 9x - 18 = 0
[by factorisation method]
⇒ 2x2 - 12x + 3x - 18 = 0

##### Correct Option: C

Given equation is 2x2 - 9x - 18 = 0
[by factorisation method]
⇒ 2x2 - 12x + 3x - 18 = 0
⇒ 2x(x - 6) + 3(x - 6) = 0
⇒ (2x + 3) (x - 6) = 0
∴ x = -3/2, 6

1. If one root of x2 - 6kx + 5 = 0 is 5, find the value of k.
1. -1/2
2. -1
3. 1
4. 2

1. Given, one root of x2 - 6kx + 5 = 0 is 5.
∴ x = 5 satisfies x2 - 6kx + 5 = 0

##### Correct Option: C

Given, one root of x2 - 6kx + 5 = 0 is 5.
∴ x = 5 satisfies x2 - 6kx + 5 = 0
⇒ 52 - 30k + 5 = 0
⇒ 25 - 30k + 5 = 0
⇒ 30 - 30k = 0
⇒ 30k = 30
∴ k = 1

1. Find the roots of the equation 2x2 - 11x + 15 = 0
1. 3 and 5/2
2. -3 and -5/2
3. 5 and 3/2
4. -5 and -3/2

1. 2x2 -11x + 15 = 0
[by factorisation method]
⇒ 2x2 - (6x + 5x) + 15 = 0

##### Correct Option: A

2x2 -11x + 15 = 0
[by factorisation method]
⇒ 2x2 - (6x + 5x) + 15 = 0
⇒ 2x2 - 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.