निम्नलिखित समीकरणों को गुणनखंड विधि द्वारा हल कीजिए :
(i) (2x + 3) (x + 2) = 0 (ii) x² + 3x – 18 = 0
(iii) 3x² – 4x – 7 =0 (iv) x² – 5x – 6 = 0
(v) 25x² – 10x + 1 = 0 (vi) 4x² – 8x + 3 = 0
Answers
Answer:
i)x= -3/2 or x= -2
ii) x = -6 or 3
iii)x= 7/3 or -1
iv) x = 6 or -1
v) x= 1/5
vi) x = 3/2 or 1/2
Step-by-step explanation:
i) Given that, (2x + 3)(x + 2) = 0
∴ Either, or, [∵a*b =0, then either a= 0 or b =0 ]
2x + 3 = 0 x + 2 = 0
⇒2x = -3 ⇒ x = -2
⇒x= -3/2
∴ x= -3/2 or -2
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ii)x² + 3x - 18 = 0
⇒x² + 6x - 3x - 18 = 0
⇒x(x+6) -3(x+6) = 0
⇒(x+6)(x-3)=0
Either, or,
x+6 =0 x-3 =0
⇒x = -6 ⇒x = 3
∴x = -6 or 3
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iii)3x² - 4x -7 =0
⇒3x²-7x+3x-7=0
⇒x(3x -7)+1(3x -7)=0
⇒(3x - 7)(x + 1)= 0
Either, or,
3x -7 = 0 x + 1 = 0
⇒3x = 7 ⇒x = -1
⇒x = 7/3
∴x = 7/3 or -1
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iv)x² - 5x - 6 = 0
⇒x² - 6x + x - 6 =0
⇒x(x-6) +1 (x-6) = 0
⇒(x -6)(x + 1) = 0
Either, or,
x - 6 =0 x + 1 =0
⇒x=6 ⇒x = -1
∴x = 6 or -1
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v) 25x² - 10x + 1 = 0
⇒25x² - 5x - 5x + 1 = 0
⇒5x(5x - 1) -1 (5x -1) =0
⇒(5x-1)(5x-1) = 0
⇒(5x-1)² = 0
∴5x - 1 = 0
⇒5x = 1
⇒x = 1/5
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vi) 4x² - 8x + 3 =0
⇒4x² - 6x - 2x +3 = 0
⇒2x(2x - 3) -1(2x - 3) =0
⇒(2x - 3)(2x - 1)=0
Either, or,
2x - 3 =0 2x - 1 =0
⇒2x = 3 ⇒2x = 1
⇒x=3/2 ⇒x=1/2
∴x = 3/2 or 1/2
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