Question 1(vi)
Check whether the following are quadratic equations:
(vi) $x^{2} + 3 x + 1 = (x - 2)^{2}$

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Solution

(vi) $x^{2} + 3 x + 1 = (x - 2)^{2} \Rightarrow x^{2} + 3 x + 1 = x^{2} + 4 - 4 x \Rightarrow 7 x - 3 = 0$
It is not of the form $a x^{2} + b x + c = 0$ .
Hence, the given equation is not a quadratic equation.

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Similar questions

Q. Check whether the following are Quadratic equations

x^{2} + 3 x + 1 = {(x - 2)}^{2}

Q. Check whether the following is quadratic equation.

x^{2} + 3 x + 1 = (x - 2)^{2}

Question 1(i)
Check whether the following are quadratic equations:
$(i) (x + 1)^{2} = 2 (x - 3)$

Q. Check whether the following equations are quadratic?

x + \frac{1}{x} + x^{2}, x \neq 0

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

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Quadratic Equations

Standard X Mathematics

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Question 1(vi) Check whether the following are quadratic equations: (vi) x2+3x+1=(x−2)2

(vi) x2+3x+1=(x−2)2⇒x2+3x+1=x2+4−4x⇒7x−3=0 It is not of the form ax2+bx+c=0. Hence, the given equation is not a quadratic equation.

Question 1(vi)
Check whether the following are quadratic equations:
(vi) $x^{2} + 3 x + 1 = (x - 2)^{2}$

(vi) $x^{2} + 3 x + 1 = (x - 2)^{2} \Rightarrow x^{2} + 3 x + 1 = x^{2} + 4 - 4 x \Rightarrow 7 x - 3 = 0$
It is not of the form $a x^{2} + b x + c = 0$ .
Hence, the given equation is not a quadratic equation.