Question

The roots of 2x²-5x+3=0​

Answer 1

Answer:

Roots are : 1 and 3/2

Step-by-step explanation:

Nature of roots : unequal and real

Answer 2

Answer:

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Step-by-step explanation:

${2x}^{2} + 5x + 3 = 0$

$⟹ \: \: \: \: {x}^{2} + \frac{5}{2} x + \frac{3}{2} = 0$

$⟹ \: \: \: \: {x}^{2} + 2. \frac{1}{2} . \frac{5}{2} x + ( \frac{5}{4 } {)}^{2} - {( \frac{5}{4}) }^{2} + \frac{3}{2} = 0$

$⟹ \: \: \: \: \: \: {(x + \frac{5}{4} )}^{2} - \frac{25}{16} + \frac{3}{2} = 0$

$⟹ \: \: \: \: \: \: {(x + \frac{5}{4} )}^{2} + \frac{24 - 25}{16} = 0$

$⟹ \: \: \: \: \: \: {(x + \frac{5}{4}) }^{2} - \frac{1}{16} = 0$

$⟹ \: \: \: \: \: {(x + \frac{5}{4}) }^{2} = \frac{1}{16}$

Taking square root of both sides,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + \frac{5}{4} = ± \sqrt{ \frac{1}{16} }$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + \frac{5}{4} = ± \frac{1}{4}$

Taking +ve sing,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + \frac{5}{4} = \frac{1}{4}$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{1}{4} - \frac{5}{4} = \frac{1 - 5}{4}$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{ - 4}{4} = - 1$

Taking - ve sing,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + \frac{5}{4} = - \frac{1}{4}$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - \frac{1}{4} - \frac{5}{4}$

$⟹ \: \: \: \: \: \: \: \: \: \: \: x = \frac{ - 1 - 5}{4} = \frac{ - 6}{4} = \frac{ - 3}{2}$

$∴ \: \: \: \: \: \: \: \: \: \: x = - 1 \: \: \: , \frac{ - 3}{2} .$