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  • Which of the following is not a quadratic equation ?Option: 1 <img alt="x^2-4x+2=0" src="https://learn.careers360.com/latex-image/?x%5E2-4x&plus;

Which of the following is not a quadratic equation ?

Option: 1

x^2-4x+2=0


Option: 2

x+\frac{1}{x}=1


Option: 3

x^2+\frac{1}{x}=4


Option: 4

x^2=4x


Answers (1)

best_answer

 

 

Introduction -

In the standard form of a quadratic equation \mathrm{a x^{2}+b x+c=0}

  1. All the terms (except zero) are on one side of equal (=) and zero (0) is on the other side of the equal sign.

  2. The powers of x are in descending order. 

  3. Either or both ‘b’ and ' c’ can be equal to zero but a ≠ 0 . Therefore a quadratic equation may be in the form a x^{2}+b x=0,\; a x^{2}+c=0, \;a x^{2}=0\;\text{ or } \;x^{2}=0.

  4. The term of x2 (i.e. ax2 ), the term of x (i.e. bx ), or constant term (i.e. c ) can not be more than one.

If not so, then by adding/subtracting the like terms or taking the common factor from like terms, we convert the quadratic equation in the standard form, in which there is no more than one term of x2, x, and the constant term. 

-

 

 

(a) p(x)=x^{2}-4 x+2 is a quadratic polynomial. x^{2}-4 x+2=0 is a quadratic equation.

(b) x+\frac{1}{x}=1 \Rightarrow \frac{x^{2}+1}{x}-1 \Rightarrow x^{2}+1=x \Rightarrow x^{2}-x+1=0

It is a quadratic equation

(c) x^{2}+\frac{1}{x}=1 \Rightarrow \frac{x^{3}+1}{x}=1 \Rightarrow x^{3}+1=x \Rightarrow x^{3}-x+1=0

Here, x^{3}-x+1 is a polynomial of degree 3 . Hence, x^{3}-x+1=0 is not a quadratic equation.

(d) x^2=4x can be written as x^2-4x = 0, it is a quadratic equation 

Posted by

Ritika Jonwal

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