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ICSE Class X Math 2014 Paper

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Question : 42 of 52
Marks: +1, -0
Solve for xx using the quadratic formula. Write your answer correct to two significant figures. (x−1)2−3x+4=0(x-1)^2-3x+4=0 .
Solution:  
Given:     (x−1)2−3x+4=0\;\; (x-1)^2-3x+4=0
⇒x2+1−2x−3x+4  =0\Rightarrow x^2+1-2x-3x+4\;=0
⇒  x2−5x+5  =0\Rightarrow\;x^2-5x+5\;=0
Comparing with ax2+bx+c=0ax^2+bx+c=0 , we get a=a= 1,b=−5,c=51, b=-5, c=5 .
  ∴    x=−b±b2−4ac2a\;\therefore\;\; x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}
  x=−(−5)±(−5)2−4(1)(5)2×1\;x=\frac{-(-5) \pm \sqrt{(-5)^2-4(1)(5)}}{2 \times 1}
  =5±25−202=5±52\;=\frac{5 \pm \sqrt{25-20}}{2}=\frac{5 \pm \sqrt{5}}{2}
  =5±2.2362\;=\frac{5 \pm 2.236}{2}
  =5+2.2362   and   5−2.2362\;=\frac{5+2.236}{2} \;\text{ and }\; \frac{5-2.236}{2}
  =7.2362   and   2.7642\;=\frac{7.236}{2} \;\text{ and }\; \frac{2.764}{2}
  =3.618   and   1.382\;=3.618 \;\text{ and }\; 1.382
  =3.62   and   1.38\;=3.62 \;\text{ and }\; 1.38
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