Question

Answer these questions

Answer 1

Hope u like my process
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Note::
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Here ± indicates that it can be + or -.
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4)

The root of the quadratic equation

½x² - 3x +5 =0 is a complex number and has an imaginary part.

=> (3 ± i)
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5)

For getting equal roots,

The quadratic equation should be in a form of

x² ± 2xy + y² =0____(1)

So,

$= > px(x - 3) + 9 = 0 \\ \\ or. \: \: p {x}^{2} - 3px + 9 = 0 \\ \\ or. \: \: {x}^{2} - \frac{3px}{p} + \frac{9}{p} = 0 \\ \\ or. \: \: {x}^{2} - 3x + \frac{9}{p} = 0 \\ \\ or. \: \: {(x)}^{2} - 2 \times x \times \frac{3}{2} + {( \frac{3}{ \sqrt{p} }) }^{2} = 0 \\ \\ thus \: \: by \: \: comparing \: \: to \: \: equation \: \: 1 \: \: we \: \: get \\ \\ = > \frac{3}{2} = \frac{3}{ \sqrt{p} } \\ \\ or. \: \: \sqrt{p} = 2 \\ \\ or. \: \: p = {2}^{2} = 4.... < answer > ....$

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