Find which of the following equations are quadratic:

$(B) 5 x^{2} - 8 x = - 3 (7 - 2 x)$

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Solution

Step: Finding whether the given equation is quadratic or not:

The standard form of a quadratic equation is $a x^{2} + b x + c = 0$ , where a, b and c are all real numbers and $a \neq 0$ .

Given equation is:
$5 x^{2} - 8 x = - 3 (7 - 2 x)$

$\Rightarrow 5 x^{2} - 8 x = - 21 + 6 x$

$\Rightarrow$ $5 x^{2} - 8 x - 6 x + 21 = 0$

$\Rightarrow$ $5 x^{2} - 14 x + 21 = 0;$

The given equation is of the form $a x^{2} + b x + c = 0$ ,

$∴$ Given equation is a quadratic equation.

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(E)

7 x^{3} - 2 x^{2} + 10 = (2 x - 5)^{2}

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\sqrt{{5 x}^{2} - 8 x + 3} - \sqrt{{5 x}^{2} - 9 x + 4} = \sqrt{({2 x}^{2} - 2 x)} - \sqrt{({2 x}^{2} - 3 x + 1)}

9^{{log}_{3} (1 - 2 x)} = 5 x^{2} - 5

Find the solution to the following system of linear equations:

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x-2y+3=0

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- 21 x^{2} + 16 x + 5

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