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Question

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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
Verified

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.

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