# Standard Form of a Quadratic Equation

## Trending Questions

**Q.**If ax2+bx+c=0 is a quadratic equation, then which of the following conditions is always correct?

- a, b, c are integers
- a=0
- a≠0 and a, b, c are real numbers
- b, c≠0

**Q.**A quadratic polynomial may not have zeroes.

- True
- False

**Q.**If discriminant of a quadratic equation is less than zero, then the equation has

- real and distinct roots
- real and equal roots
- no real roots
- None of the above

**Q.**In the question, a statement of assertion (𝐀) is followed by a statement of reason (𝐑). Mark the correct choice.

Assertion: The value of 𝒙 are −a2, 𝒂 for a quadratic equation 2x2+ax−a2=0.

Reason: For quadratic equation ax2+bx+c=0, x=−b±√b2−4ac2a

- Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).

- Assertion (A) is false, but reason (R) is true.

- Assertion (A) is true, but reason (R) is false.

- Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).

**Q.**

Check Whether The Following Are Quadratic Equations$(2\mathrm{X}\xe2\u02c6\u20191)(\mathrm{X}\xe2\u02c6\u20193)=(\mathrm{X}+5)(\mathrm{X}\xe2\u02c6\u20191)$.

**Q.**What is the degree of a quadratic polynomial?

- 1
- 3
- 2
- 0

**Q.**

What is the degree of a quadratic equation?

**Q.**

What are quadratic equation? Give example

**Q.**

Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

x

^{2}– 5x + 32 = 0x

^{2}– 40x + 124 = 0x

^{2}– 45x + 324 = 0x

^{2}– 4x+ 32 = 0

**Q.**

A rectangular field has an area of 3 sq. units. The length is one unit more than twice the breadth. Frame an equation to represent this. [Assume breadth is x].

2x2+x−3=0

2x2+x−6=0

x2–2x+3=0

x2–2x+6=0

**Q.**A real number α is said to be the root of the quadratic equation ax2+bx+c=0, if aα2+bα+c=0

- True
- False

**Q.**Match the value of the expression x99+x100+x for the given values of x.

- 3
- -1
- \N

**Q.**Question 2

Which of the following is not a quadratic equation?

(a) 2(x−1)2=4x2−2x+1

(b) 2x−x2=x2+5

(c) (√2x+√3)3=3x2−5x

(d) (x2+2x)2=x4+3+4x2

**Q.**

Which of the following is the standard form of a quadratic equation?

ax2+c=0; a≠0; a & c are real

ax2+bx+c=0;a≥0; a, b, c are real

ax2+bx+c=0; a ≠ 0; a, b, c are real

ax2+bx+c=0;a≤0; a, b, c are real.

**Q.**Question 1(iii)

Check whether the following are quadratic equations:

(iii)(x−2)(x+1)=(x−1)(x+3)

**Q.**

Which of the following is not a quadratic equation?

0x2 – 2x=x2+3x+5

2(x+1)+8=(x+2)(x−2)

x2 + 4x+4=x2–4

x(2x+3)=x2+1

**Q.**The coefficient of x in the quadratic equation ax2+bx+c=0 is called the linear coefficient.

- True
- False

**Q.**If ax2+bx+c=0 is a quadratic equation, then which of the following conditions is always correct?

- a, b, c are integers
- a=0
- a≠0 and a, b, c are real numbers
- b, c≠0

**Q.**

The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say x toys were produced on a day, what is the total cost of production in terms of x?

(x-55)(x+55)

x

^{2 }- 55xx

^{2}+ 55x55x – x

^{2}

**Q.**If discriminant of a quadratic equation is equal to zero, then the equation has

- real and equal roots
- no real roots
- real and distinct roots
- None of the above

**Q.**What are the condition(s) for (a2−4)xd−2+bx+c=0

to be a quadratic equation in x?

- a can be ANY real number other than 2, -2
- a, b, c are ALL real numbers where a cannot be 4 or -4
- d = 4
- a, b, c are real

**Q.**

If ax2+bx+c=0 is a quadratic equation, then “a” cannot be:

0

-1

π

1

**Q.**

The expression x4+8x2+16 can be factorized as:

(x2+x+16)2

(x2+x+1)2

(x2+4)2

(x2+x−4)(x2−x+4)

**Q.**

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. The mathematical representation to find out the number of toys produced on that day is:

x2 – 50x+320=0

x2 – 40x+124=0

x2 – 45x+324=0

x2– 55x+750=0

**Q.**The coefficient of x in the quadratic equation ax2+bx+c=0 is called the linear coefficient.

- True
- False

**Q.**

Which of the following is the reduced form of the equation (x−2)3 = (2x−1)2+x3 ?

**Q.**

Check whether the following is a quadratic equation: (x+2)3=2x(x2−1)

**Q.**If axn+bxn−1+c=0 is a quadratic equation, then which of the given options is not correct?

- a, b and c are real numbers
- n = 2
- Coefficient 'a' must always be 1
- a≠0

**Q.**If ax2+bx+c=0 is a quadratic equation, then which of the following conditions is always correct?

- a, b, c are integers
- a=0
- a≠0 and a, b, c are real numbers
- b, c≠0

**Q.**

Add

$8{x}^{2}+5xy-3{y}^{2},-5{x}^{2}+3xy+5xyand-3{x}^{2}+2xy+4{y}^{2}$