Quadratic Equation

Q.

Which of the following is not a quadratic equation?

1. $x^2+5x=10$

2. $(\sqrt{2}x+\sqrt{3}{)}^2=3x^2-5x$

3. $2x-x^2=x^2+5$

4. $(x^2+2x{)}^2=x^4+3+4x^2$

Q.

A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows:
The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also, he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the $2^{nd}$ digit, given that ‘b’ is the second digit?

1. $4b+5=9$

2. $b^2+2b-3=0$

3. $b^2+3b-4=0$

4. $b^3-9=0$

Q.

If $a{x}^n+b{x}^{(n-1)}-1+c=0$ is a quadratic equation, then n = ___

Q.

Form a quadratic equation for the given situation:
Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited initially. His total assets now stand at debt of 4 crore.

1. $k{x}^2-kx-4=0$

2. $x^2-4x+4=0$

3. $x^2-kx+4=0$

4. $x^2-kx-k=0$

Q.

Condition for a$x^2$ + bx + c = 0 to be a quadratic equation is

1. a≠ 0; a, b, c are real.

2. a≥ 0; a, b, c are real

3. a< 0; a, b, c are unreal

4. a≤ 0; a, b, c are real

Q.

Which of the following is not a quadratic equation?

1. x² + 5x +6
2. x² + x +7
3. x² + 13x +12
4. x² + 2x +3

Q.

Find the area of a rectangle, if the length of the rectangle is x and the breadth is twice the length.

1. A =

2. A =

3. None of these

4. A =

Q.

If a = 0, what is the degree of the equation a$x^2$ + bx + c = 0

Q.

A polynomial is given as p(x) = x² + 6x + 9. The quadratic equation for it is,

1. p(x) =0
2. p(x) =2
3. p(x) =100
4. p(x) =1

Q.

Find solution of the given equation

$\frac{x+5}{1}=\frac{2x+10}{x-6}$

1. $x=5,x=-8$

2. $x=-3,x=-5$

3. $x=8,x=-5$

4. $x=7,x=-6$