The following equation is a quadratic equation.
$3 x^{2} - 5 x + 9 = x^{2} - 7 x + 3$ (state true of false)

True

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False

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Solution

The correct option is A True
$\Rightarrow$ The given equation is $3 x^{2} - 5 x + 9 = x^{2} - 7 x + 3$
$\Rightarrow$ $3 x^{2} - 5 x + 9 = x^{2} - 7 x + 3$
$\Rightarrow$ $3 x^{2} - 5 x + 9 - x^{2} + 7 x - 3 = 0$
$\Rightarrow$ $2 x^{2} + 2 x + 6 = 0$
$\Rightarrow$ A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
$\Rightarrow$ The give equation is $2 x^{2} + 2 x + 6 = 0$
$\Rightarrow$ Comparing given equation with standard form of quadratic equation $a x^{2} + b x + c = 0$ .
$\Rightarrow$ We get, $a = 2, b = 2$ and $c = 6$
$∴$ The given equation $3 x^{2} - 5 x + 9 = x^{2} - 7 x + 3$ is quadratic equation is true.

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