What is the coefficient of X Square in X 2?

Solution:

A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable next to it. 

i) 2 + x² + x

Coefficient of x² is 1.

ii) 2 - x² + x³

Coefficient of x² is -1.

iii) (π/2)x² + x

Coefficient of x² is π/2.

iv) √2x - 1

There is no  x² term in the given expression. We can rewrite it as 0x² + √2x - 1 

Therefore, the coefficient of x² = 0, as x² doesn't exist.

☛ Check: Class 9 Maths NCERT Solutions Chapter 2


Video Solution:

Write the coefficients of x² in each of the following: (i) 2 + x² + x (ii) 2 - x² + x³ (iii) (π/2)x² + x (iv) √2x - 1

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.1 Question 2:

Summary:

The coefficients of x² in each of the following equations 2 + x²+ x, 2 - x² + x³, (π/2) x² + x, and √2x - 1 are 1, -1, π/2, and 0 respectively.


☛ Related Questions:

  • Give one example each of a binomial of degree 35, and of a monomial of degree 100.
  • Write the degree of each of the following polynomials:i) 5x3 + 4x2 + 7xii) 4 - y2iii) 5t - √7iv) 3
  • Classify the following as linear, quadratic and cubic polynomials:i) x² + x ii) x - x3iii) y + y² + 4iv) 1 + xv) 3tvi) r²vii) 7x3

Reference > Mathematics > Algebra > The Quadratic Formula

This is all well and good, this "completing the square" method (you might say) but what if the coefficient of x2 isn't a perfect square? We can't complete the square in that situation, can we?

Well, not exactly. But there is something we can do. Consider the following:

3x2 - 8x - 3 = 0

3 is not a perfect square, but suppose we took this equation and multiplied both sides by 3...then we would have the following:

9x2 - 24x -9 = 0

What do we need to do to complete the square now? The constant term needs to be 16, and since it's -16, we need to add 25:

9x2 - 24x + 16 = 25
(3x - 4)2 = 52
3x - 4 = 5 or 3x - 4 = -5
3x = 9 or 3x = -1
x = 3 or x = -1/3

Problem #1
Solve for x if 2x2 + x - 15 = 0

Solution #1
If we multiply the entire equation by 2, we get:

4x2 + 2x - 30 = 0

Thus, to complete the square, the constant term must be 1/4. Since it's -30 (or -120/4), we need to add 121/4 to both sides:

4x2 + 2x - 30 + 121/4 = 121/4
4x2 + 2x + 1/4 = 121/4
(2x + 1/2)2 = (11/2)2
2x + 1/2 = 11/2 or 2x + 1/2 = -11/2
2x = 10/2 or 2x = -12/2
x = 5/2 or x = -3

Problem #2
Solve for x if 12x2 - 13x - 4 = 0

Solution #2
You might be tempted to multiply this by 12 to make a perfect square (144), but that's really overkill! Because if we multiply 12 by 3, we get 36, which is also a perfect square. [HINT: in the prime factorization of 12, 3 is the only prime factor which doesn't have an even exponent - that's why I thought to multiply by 3]

So we have 36x2 - 39x - 12 = 0

To have a completed square, the constant term must be (13/4)2 or 169/16. But it's actually -12, or -192/16. Thus we need to add 361/16:

36x2 - 36x -12 + 361/16 = 0 + 361/16
36x2 - 36x + 169/16 = 361/16
(6x - 13/4)2 = (19/4)2
6x - 13/4 = 19/4 or 6x - 13/4 = -19/4
6x = 32/4 or 6x = -6/4
x = 4/3 or x = -1/4

Special Hint
Sometimes you can make the coefficient of x2 a perfect square by dividing instead of multiplying. For example, in 2x2 + 2x - 12 = 0, if you notice that all the coefficients are multiples of 2, you can divide out the two, leaving x2 + x - 6 = 0, which is much simpler.

For each problem below, solve by completing the square.

Questions

8.

(1/2)x2 + (3/2)x + 1 = 0

What is the coefficient of X Square in X 2?

Assign this reference page

Click here to assign this reference page to your students.

Solving Quadratics by Completing the Square

Results with Radicals

Blogs on This Site

What is the coefficient of X Square in X 2?

Reviews and book lists - books we love!

What is the coefficient of X Square in X 2?

The site administrator fields questions from visitors.

Like us on Facebook to get updates about new resources

What is the coefficient of X in X²?

The coefficient of x will be 0 because in this expression there is no variable x. The coefficient of x2 is -1.

What is the coefficient of x square 2?

The coefficient of x2 in −x2 is −1.

What does coefficient of x squared mean?

The coefficient of x^2 tells you a lot about the shape of the quadratic. Firstly, a positive coefficient implies there is a minima (often known as a smiley graph) and a negative coefficient implies there is a maxima (often known as a sad graph). All quadratic graphs are symmetrical about their minima or maxima.

What is the coefficient of X square in the expansion of x 2 Cube?

Step-by-step explanation: Thus it's coefficient will be 0: x^2(x-2)3.