Question

Find the roots of the equation 2x²-5x+3=0, by factorisation. ​

Answer 1

Answer:

2x²- 5x + 3 = 0

2x² -2x - 3x +3 = 0

2x(x - 1) - 3(x - 1) = 0

2x - 3 = 0 x - 1 = 0

2x = 3 x = 1

x = 3/2

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Answer 2

Equation :

$\tt {{2x}^2 - 5x + 3= 0 }$

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

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$: \implies \tt {2x(x-1) - 3(x-1)=0 }$

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$:\implies \tt {{2x - 3}{x - 1}=0}$

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$: \implies \tt{ 2x - 3 = 0 }$ ㅤㅤ

$: \implies \tt { x = \frac {3}{2}}..............(1)$

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$: \implies \tt {x - 1= 0}$

$: \implies \tt { x = 1 }.................(2)$

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ㅤ$\bf { x = \frac {3}{2} \: and \: 1 \: are \: the \: roots \: of \: the \: equation }$

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$\rule {200}4$

Verification :

2x² - 5x + 3 = 0

↬p(x) = 1

↬ 2(1)² - 5(1) + 3 = 0

↬ 2 - 5 + 3 =0

↬ 0 = 0

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p(x)=(3/2)

↬2(3/2)² - 5(3/2) + 3 = 0

↬ 2(9/4) - 15/2 + 3 =0

↬ 9/2 - 15/2 + 3 =0

↬ -3 + 3 =0

↬0= 0

Hence, verified. ☑

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