Question

3x²-17x+20=0 quadratic equation Factorisation method​

Answer 1

Answer:

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Step-by-step explanation:

question must be : 3x²-17x-20

Answer 2

Answer:-

$\red{\bigstar}$$\large\boxed{\tt\purple{x = 4}}$

$\red{\bigstar}$$\large\boxed{\tt\purple{x = \dfrac{5}{3}}}$

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• Given:-

$\sf 3x^2 - 17x + 20 = 0$

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• Solution:-

Given,

$\sf 3x^2 - 17x + 20 = 0$

Now,

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✴ Concept Understanding:-

Firstly we need to split the middle term in order to form pairs.

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✯ Some rules to keep in mind while splitting the middle term:-

1.) The split middle term should sum upto the original middle term.

2.) The product of the split middle terms should be equal to the product of first and the last term.

3.) In order to split the middle term we need to find the product of first and the third term and take out their factors.

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Similarly here,

✯ Product of 1st and the last term will be 20 × 30 = 60

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Now Factorising,

$\begin{array}{r | l}2 & 60 \\ \cline{2-2} 2 & 30 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1 \end{array}$

We get the factors of 60 as 2×2×3×5

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Now, arranging these factors in such pairs that their product is 60 and they sum upto 17 (the original middle term).

Hence,

Such a possible pair will be,

✯ 3x²-12x-5x+20

Here,

-12 and -5 sum upto 17 and their product is also 60.

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• Further solving the Question:-

➪ $\sf 3x^2 - 12x - 5x + 20 = 0$

➪ $\sf 3x(x - 4) - 5(x - 4) = 0$

➪ $\sf (x-4) (3x-5) = 0$

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Now,

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➪ $\sf x - 4 = 0$

★ $\bf\pink{x = 4}$

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Also,

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➪ $\sf 3x - 5 = 0$

➪ $\sf 3x = 5$

★ $\bf\pink{x = \dfrac{5}{3}}$

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Therefore, the value of x is 4 and 5/3.