Check whether the following are Quadratic equations
$(x - 3) (2 x + 1) = x (x + 5)$

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Solution

$(x - 3) (2 x + 1) = x (x + 5)$
$2 x^{2} + x - 6 x - 3 = x^{2} + 5 x$
$\Rightarrow 2 x^{2} + x - 6 x - 3 - x^{2} - 5 x = 0$
$\Rightarrow x^{2} - 10 x - 3 = 0$ has its highest power $2$
Hence it is a quadratic equation.

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Q. Question 1(iv)
Check whether the following are quadratic equations:

(i v) (x - 3) (2 x + 1) = x (x + 5)

Q. Check whether the following in quadratic equation.

(x - 3) (2 x + 1) = x (x = 5)

Check whether the following is a quadratic equation.

(x - 3) (2 x + 1) = x (x + 5)

Check whether the following are quadratic equations

1) (x-3) (2x+1) = x(x+5)

2) x*2+3x+1=(x-2)*2

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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Check whether the following are Quadratic equations(x−3)(2x+1)=x(x+5)

(x−3)(2x+1)=x(x+5)2x2+x−6x−3=x2+5x⇒2x2+x−6x−3−x2−5x=0⇒x2−10x−3=0 has its highest power 2Hence it is a quadratic equation.

Check whether the following are Quadratic equations
$(x - 3) (2 x + 1) = x (x + 5)$

$(x - 3) (2 x + 1) = x (x + 5)$
$2 x^{2} + x - 6 x - 3 = x^{2} + 5 x$
$\Rightarrow 2 x^{2} + x - 6 x - 3 - x^{2} - 5 x = 0$
$\Rightarrow x^{2} - 10 x - 3 = 0$ has its highest power $2$
Hence it is a quadratic equation.