. Solve the following quadratic equations by factorization:
i)X 2 - 18 x+77 =0 ii) 9x 2 +6x+1 =0 iii) 4x 2 -12x+9 =0
iv) √2 x 2 +7x+5 √2 =0
Answers
Answer:
hello frnd this may be helpful. if u spot any mistakes sry for that
Answer
i) The solutions are 7 and 11
ii) -1/3 and -1/3
iii) 3/2 and 3/2
iv) -5/√2 and - √2
Solutions
i) x² - 18x + 77 =0
Splitting the middle term →
⇒ x² - 7x - 11x + 77= 0
⇒x(x - 7) - 11(x - 7) =0
⇒(x - 7)(x - 11)
Therefore the solutions are
x - 7 = 0 and x - 11 = 0
⇒ x = 7 and ⇒x = 11
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ii) 9x² + 6x + 1 = 0
Splitting the middle term
⇒ 9x² + 3x +3x +1 =0
⇒ 3x(3x + 1) + 1(3x +1)=0
⇒ (3x + 1)(3x +1)
Therefore the solutins are
3x + 1= 0 and 3x +1=0
⇒ 3x = -1 and ⇒3x = -1
⇒x = -1/3 and ⇒x = -1/3
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iii) 4x² -12x + 9 = 0
Splitting the middle term
⇒4x² - 6x - 6x + 9 = 0
⇒ 2x(2x - 3) -3(2x - 3) = 0
⇒(2x - 3)(2x - 3) = 0
Therefore the solutions are
2x - 3= 0 and 2x - 3 =0
⇒ 2x = 3 and ⇒2x = 3
⇒x = 3/2 and ⇒x = 3/2
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iv) √2x² + 7x + 5√2 = 0
Splitting the middle term
⇒√2x² + 2x + 5x + 5√2 = 0
⇒√2x(x + √2) + 5(x + √2 = 0
⇒(√2x + 5)(x +√2)= 0
Therefore the solutins are
√2x + 5 = 0 and x + √2 = 0
⇒√2x = -5 and ⇒ x = - √2
⇒x = -5/√2
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