(A) Given equation: $(x-2)^{2}+1=2x-3$Expand the left side using the identity $(a-b)^{2} = a^{2}-2ab+b^{2}$:$(x^{2}-4x+4)+1=2x-3$$x^{2}-4x+5=2x-3$Brin

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Yes,it is a quadratic equation.

(A) Given equation: $(x-2)^{2}+1=2x-3$Expand the left side using the identity $(a-b)^{2} = a^{2}-2ab+b^{2}$:$(x^{2}-4x+4)+1=2x-3$$x^{2}-4x+5=2x-3$Bring all terms to one side to set the equation to zero:$x^{2}-4x-2x+5+3=0$$x^{2}-6x+8=0$Since this equation is in the form $ax^{2}+bx+c=0$ where $a \neq 0$,it is a quadratic equation.

Class 10 Mathematics Quadratic Equations Quadratic Equations

Easy

Examine whether the following equation is quadratic or not: $(x-2)^{2}+1=2x-3$.

A
Yes,it is a quadratic equation.
B
No,it is not a quadratic equation.
C
It is a linear equation.
D
It is a cubic equation.

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Quadratic Equations

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Quadratic Equations

Which of the following is not a quadratic equation?

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Obtain the roots of the following equation using the method of 'completing the square': $5x^{2} - 4x - 10 = 0$.

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Verify whether the given value of $x$ is a solution of the quadratic equation or not: $(x-2)(x+3)+1=0$; $x=2$.

Medium

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If $\frac{1}{2}$ is a root of the equation $x^{2}+kx-\frac{5}{4}=0$,then the value of $k$ is

Easy

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Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{6}, x = 5$

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Examine whether the following equation is quadratic or not: $(x-2)^{2}+1=2x-3$.

Similar Questions

Which of the following is not a quadratic equation?

Obtain the roots of the following equation using the method of 'completing the square': $5x^{2} - 4x - 10 = 0$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $(x-2)(x+3)+1=0$; $x=2$.

If $\frac{1}{2}$ is a root of the equation $x^{2}+kx-\frac{5}{4}=0$,then the value of $k$ is

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{6}, x = 5$

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