Math, asked by PKV81, 10 months ago

factorise the given photo



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Answers

Answered by RvChaudharY50
19

To Find :-

  • Factorise 21x² - 4√5x - 5 ?

Solution :-

Before Factorising Put The Equation Equal to Zero.

Now,

21x² - 4√5x - 5 = 0

Splitting The Middle Term now, we get,

21x² - 7√5x + 3√5x - 5 = 0

→ 7x(3x - √5) + √5(3x - √5) = 0

→ (3x - √5)(7x + √5) = 0

Putting Both Equal to Zero now, we get,

3x - √5 = 0

→ 3x = √5

→ x = (√5/3).

Or,

(7x + √5) = 0

→ 7x = (-√5)

→ x = (-√5/7) .

Hence , x { (5/3) , (-5/7) }.

Answered by MяƖиνιѕιвʟє
7

Factorising by Splitting middle term

 \implies \: 21 {x}^{2}  - 4 \sqrt{5x}  - 5 = 0 \\  \\  \implies \: 21 {x}^{2}  - 7 \sqrt{5x}   + 3 \sqrt{5} x - 5 = 0 \\  \\  \implies \: 7x(3x -  \sqrt{5} ) +  \sqrt{5} (3x -  \sqrt{5} ) \\  \\  \implies \: (7x +  \sqrt{5} )(3x -  \sqrt{5} ) = 0 \\  \\  \implies(7x +  \sqrt{5} ) = 0 \: or \: (3x -  \sqrt{5} ) = 0 \\  \\  \implies \: x =  \frac{ -  \sqrt{ 5} }{7} \:  or \: x =  \frac{ \sqrt{5} }{3}  \\  \\

By using Formula :-

On comparing the above questions with

 \implies \: a {x}^{2}  + bx + c = 0

We get,

a = 21. , b = -45. , c = -5

We know that,

D = b^2 - 4ac

 \implies \:  {( - 4 \sqrt{5}) }^{2} - 4 \times 21 \times ( - 5) \\  \\  \implies \: 80 + 420 = 500

From this we have

D = √500 = 105

Now,

We have a formula to find zeroes of a quadratic polynomial

Put the above value in this formula, we get

 \implies \: x \:  =  \frac{  -  b \: \pm \:  \sqrt{d}  }{2a}  \\  \\  \implies \: x \:  =  \frac{ - ( - 4 \sqrt{5} ) + 10 \sqrt{5} }{2 \times 21}  \: or \: x \:  =  - \frac{ - ( - 4 \sqrt{5} ) - 10 \sqrt{5} }{2 \times 21}  \\  \\  \implies \: x =  \:  \frac{4 \sqrt{5}  + 10 \sqrt{5} }{42}  \: or \: x =  \frac{4 \sqrt{5} - 10 \sqrt{5}  }{42}  \\  \\  \implies \: x =  \frac{14 \sqrt{5} }{42}  \: or \: x =  \frac{ - 6 \sqrt{5} }{42}  \\  \\  \implies \: x \:  =   \frac{ \sqrt{5} }{3}  \: or \: x  =  \frac{ -  \sqrt{5} }{7}

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