Which of the following equations, is not a quadratic equation ?
A. \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 7x + 3 = 0}}\]
B. \[{\text{3}}{{\text{x}}^{\text{2}}}{\text{ - 4x + 1 = 0}}\]
C. \[{\text{2x - 7 = 0}}\]
D. \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 3 = 0}}\]
Answer
363.3k+ views
Hint: Let us check each of the given options whether that is a quadratic equation or not by the definitions of different types of polynomial equation. Check the highest power of x that represents the degree of the polynomial function.
Complete step-by-step answer:
As we know that the highest degree of any polynomial equation decides which type of equation that is,
And the highest degree is the highest power of the variable (like x) in that equation.
So, the highest power of x in the polynomial equation is 1. Then the equation will be linear like 3a + b = 0 is the linear equation in x.
The highest power of x in the polynomial equation is 2. Then the equation will be quadratic like \[{\text{a}}{{\text{x}}^{\text{2}}}{\text{ + bx + c = 0}}\] is the quadratic equation in x
The highest power of x in the polynomial equation is 3. Then the equation will be cubic like \[{\text{a}}{{\text{x}}^3}{\text{ + b}}{{\text{x}}^2}{\text{ + cx + d = 0}}\] is the cubic equation in x
And, if the highest power of x in the polynomial equation is 4. Then the equation will be biquadratic like \[{\text{a}}{{\text{x}}^4}{\text{ + b}}{{\text{x}}^3}{\text{ + c}}{{\text{x}}^2}{\text{ + dx + e = 0}}\] is the biquadratic equation in x.
So, now we had to check the highest degree in all the options.
Option A ( \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 7x + 3 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Option B ( \[{\text{3}}{{\text{x}}^{\text{2}}}{\text{ - 4x + 1 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Option C ( \[{\text{2x - 7 = 0}}\] ) will be a linear equation because the highest degree of x is 1.
Option D ( \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 3 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Hence equation at option C is not a quadratic equation.
So, the correct option will be C.
Note: Whenever we come up with this type of problem then the easiest and efficient way to check whether the given equation is quadratic or not is by checking the highest degree of x in the given equation. If the highest degree is 2 then the equation will be quadratic otherwise the given equation will not be a quadratic equation.
Complete step-by-step answer:
As we know that the highest degree of any polynomial equation decides which type of equation that is,
And the highest degree is the highest power of the variable (like x) in that equation.
So, the highest power of x in the polynomial equation is 1. Then the equation will be linear like 3a + b = 0 is the linear equation in x.
The highest power of x in the polynomial equation is 2. Then the equation will be quadratic like \[{\text{a}}{{\text{x}}^{\text{2}}}{\text{ + bx + c = 0}}\] is the quadratic equation in x
The highest power of x in the polynomial equation is 3. Then the equation will be cubic like \[{\text{a}}{{\text{x}}^3}{\text{ + b}}{{\text{x}}^2}{\text{ + cx + d = 0}}\] is the cubic equation in x
And, if the highest power of x in the polynomial equation is 4. Then the equation will be biquadratic like \[{\text{a}}{{\text{x}}^4}{\text{ + b}}{{\text{x}}^3}{\text{ + c}}{{\text{x}}^2}{\text{ + dx + e = 0}}\] is the biquadratic equation in x.
So, now we had to check the highest degree in all the options.
Option A ( \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 7x + 3 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Option B ( \[{\text{3}}{{\text{x}}^{\text{2}}}{\text{ - 4x + 1 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Option C ( \[{\text{2x - 7 = 0}}\] ) will be a linear equation because the highest degree of x is 1.
Option D ( \[{\text{4}}{{\text{x}}^{\text{2}}}{\text{ - 3 = 0}}\] ) will be a quadratic equation because highest degree of x is 2.
Hence equation at option C is not a quadratic equation.
So, the correct option will be C.
Note: Whenever we come up with this type of problem then the easiest and efficient way to check whether the given equation is quadratic or not is by checking the highest degree of x in the given equation. If the highest degree is 2 then the equation will be quadratic otherwise the given equation will not be a quadratic equation.
Last updated date: 03rd Oct 2023
•
Total views: 363.3k
•
Views today: 7.63k
Recently Updated Pages
What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
