Quadratic Equation Any equation is in the form of $ax^2 + bx + c = 0$ where $a \neq 0$ is a quadratic equation. Q1: Check whether the following are quadratic equations: (i) $(x+1)^2 = 2(x-3)$

Answer: Yes, the given equation $(x+1)^2 = 2(x-3)$ is a quadratic equation.

Step-by-step solution

Step 1: Expand the equation

To determine if the given equation is a quadratic equation, we first need to expand both sides of the equation and simplify it. We will use the algebraic identity $(a+b)^2 = a^2 + 2ab + b^2$ for the left side and the distributive property for the right side.

Step 2: Simplify both sides

Applying the identity $(x+1)^2 = x^2 + 2(x)(1) + 1^2 = x^2 + 2x + 1$ and distributing on the right side $2(x-3) = 2x - 6$ , we get the simplified form of the equation.

Step 3: Rearrange into standard form

Now, we move all terms from the right side of the equation to the left side to set the equation to zero. This allows us to combine like terms and express the equation in the standard quadratic form $ax^2 + bx + c = 0$ .

Step 4: Identify coefficients and conclude

The simplified equation is $x^2 + 7 = 0$ . Comparing this to the standard form of a quadratic equation, $ax^2 + bx + c = 0$ , we can identify the coefficients. Here, $a=1$ , $b=0$ , and $c=7$ . Since the coefficient of $x^2$ (which is $a$ ) is $1$ (and not zero), the equation is indeed a quadratic equation.

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Quadratic Equation Any equation is in the form of ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 where a≠0a \neq 0a=0 is a quadratic equation. Q1: Check whether the following are quadratic equations: (i) (x+1)2=2(x−3)(x+1)^2 = 2(x-3)(x+1)2=2(x−3)