Question

factorise 3x square+2x-5=0​

Answer 1

Answer:

718168261181yi11y176

Answer 2

$\large\sf\underline{Given\::}$

• $\sf\:3x^{2}+2x-5=0$

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$\large\sf\underline{To\::}$

• Factorise the given equation.

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$\large\sf\underline{How\:do\:we\:factorise\:?}$

Factorising a quadratic equation means to break the given expression into its product form.

To factorise $\sf\:ax^{2}+bx+c$ we need to :

• Multiply c and a if the expression is complicated otherwise we can proceed simply by searching for such term whose sum or difference gives us the middle term.

• The number which we get as product by multiplying c and a , need to be broken in such a way that the sum or difference of those two numbers gives us the middle number.

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$\large\sf\underline{Solution\::}$

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

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• Multiplying 3 and 5 we get 15 . So we need to find such a number whose sum or difference is 2 and whose product gives us 15 .

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The two numbers are 5 and 3 and their difference gives the middle term that is 2 whereas their product 5 × 3 = 15 .

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$\sf\implies\:3x^{2}+(5-3)x-5=0$

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• Opening the brackets

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$\sf\implies\:3x^{2}+5x-3x-5=0$

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• Taking x as common from first two terms and 1 from other two terms.

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$\sf\implies\:x(3x+5)-1(3x+5)=0$

$\small{\underline{\boxed{\mathrm\pink{\implies\:(3x+5)(x-1)}}}}$ ★

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So roots of the equation are :

Case 1 :

$\sf\:3x+5=0$

$\sf\to\:3x=-5$

$\sf\to\:x=\frac{-5}{3}$

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Case 2 :

$\sf\:x-1=0$

$\sf\to\:x=1$

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!! Hope it helps !!