Question

1. Check whether the following are quadratic equations:
() (x+1)²=2(x-3)
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Answer 1

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Answer 2

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$\rm\:{(x+1)}^{2}=2(x-3)$

$\rm\longrightarrow\:{(x)}^{2}+2\times\:x\times\:1+{(1)}^{2}=2x-6$

$\rm\longrightarrow\:{x}^{2}+\cancel{2x}+1=\cancel{2x}-6$

$\rm\longrightarrow\:{x}^{2}+1=-6$

$\rm\longrightarrow\:{x}^{2}+1+6=0$

$\rm\longrightarrow\:{x}^{2}+7=0$

Hence,the given equation is a quadratic equations because it is of the form ax² + bx + c = 0.

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⤇ Quadratic Equations :- An equation of the form of ax² + bx + c = 0 where a,b,c are real numbers and a ≠ 0 is called quadratic equation in x.

⤇Roots of a quadratic equation :- A real number α is called a root of the quadratic equation ax² + bx + c = 0 ,a ≠ 0 if aα² + bα + c = 0.