(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 Mix Examples - Quadratic Equations

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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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Mix Examples - Quadratic Equations

Which of the following equations has no real roots?

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Check whether the equation $6x^2 - 7x + 2 = 0$ has real roots, and if it has, find them by the method of completing the squares.

Medium

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If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

Medium

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

Easy

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Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} = 9$.

Easy

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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 equations has no real roots?

Check whether the equation $6x^2 - 7x + 2 = 0$ has real roots, and if it has, find them by the method of completing the squares.

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

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

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} = 9$.

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