Question

Find the roots of quadratic equation 2x²-7x+3=0 by applying quadratic formula
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Answer 1

Answer:

Roots of the equation 2x² - 7x + 3 = 0 are 3 and ½

Explanation:

Given equation,

$\rm \implies \: {2x}^{2} - 7x + 3 = 0$

On comparing with the general form of a quadratic equation ax² + bx + c = 0

We get,

• a = 2
• b = -7
• c = 3

By quadratic formula,

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {( - b)}^{2} - 4ac } }{2a}$

Substituting a, b, and c :-

$\rm \implies \: x = \dfrac{ - ( -7 ) \pm \sqrt{ {( - 7)}^{2} - 4(2)(3) } }{2(2)}$

$\rm \implies \: x = \dfrac{ 7 \pm \sqrt{49 - 24 } }{4}$

$\rm \implies \: x = \dfrac{ 7 \pm \sqrt{25 } }{4}$

$\rm \implies \: x = \dfrac{ 7 \pm 5 }{4} \: and \: \dfrac{7 - 5}{4}$

$\rm \implies \: x = \dfrac{{ 7+ 5} }{4}$

$\rm \implies \: x = \dfrac{ 12 }{4} \: and \: \dfrac{2}{4}$

$\rm \implies \: x = 3 \: and \: \dfrac{1}{2}$

∴ The roots of the equation is 3 and ½

Answer 2

$\Huge \mid \underline {\rm {{{\color{blue}{Given...}}}}} \mid$

Quadratic equation is

$\bf \Large \longrightarrow \: \: 2 {x}^{2} \: - \: 7x \: + \: 3 \: = \: 0$

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$\Huge \mid \underline {\rm {{{\color{blue}{To \: \: Find...}}}}} \mid$

Roots of the Quadratic equation.

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$\Huge \mid \underline {\rm {{{\color{blue}{Solution...}}}}} \mid$

By Splitting the middle term

$\rm \leadsto \: \: 2 {x}^{2} \: - \: 7x \: + \: 3 \: = \: 0$

$\rm \leadsto \: \:2 {x}^{2} \: - \: 6x \: - x \: + \: 3 \: = \: 0$

$\rm \leadsto \: \:2x \: ( \: x \: - \: 3 \: ) \: \: - 1 \: ( \: x \: - \: 3 \: ) \: = \: 0$

$\rm \leadsto \: \:(2x - 1) \: \: \: (x - 3) \: = \: 0$

$\rm \leadsto \: \:2x \: - \: 1 \: = \: 0 \: \: \: \: \: \: ; \: \: \: \: \: \: x \: - \: 3 \: = \: 0$

$\rm \leadsto \: \:x \: = \: \frac{1}{2} \: \: \: \: \: \: \: \: ; \: \: \: \: \: \: \: \: x \: = \: 3$

Roots of the quadratic equation is 1/2 and 3.

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$\Huge \mid \underline {\rm {{{\color{blue}{Note...}}}}} \mid$

You can solve this question by second method ( Quadratic formula ) also with is already answered by @taslimuddinahmed60.