ICSE Class X Math 2014 Solved Paper

Question : 42 of 52

Marks: +1, -0

Solve for

x

using the quadratic formula. Write your answer correct to two significant figures.

(x-1)^2-3 x+4=0

Solution:

Given:

\;\; (x-1)^2-3 x+4=0

⇒ x^2+1-2 x-3 x+4\;=0

⇒\;x^2-5 x+5\;=0

Comparing with

a x^2+b x+c=0

, we get

a=

1, b=-5, c=5

\; ∴ \;\; x=\;{-b ± {√{b^2-4 a c}}}/{2 a}

\;x=\;{-(-5) ± {√{(-5)^2-4(1)(5)}}}/{2 × 1}

\;=\;{5 ± {√{25-20}}}/{2}=\;{5 ± {√{5}}}/{2}

\;=\;{5 ± 2. 236}/{2}

\;=\;{5+2. 236}/{2} \;\text " and "\; \;{5-2. 236}/{2}

\;=\;{7. 236}/{2} \;\text " and "\; \;{2. 764}/{2}

\;=3.618 \;\text " and "\; 1.382

\;=3.62 \;\text " and "\; 1.38

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