1.
Find the roots of the following quadratic equations, if they exist, by the method of
completing the square:
(i) 2x2– 7x+ 3 = 0
Answers
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2x²-7x+3=0
multiplying whole equation by 2,we get
4x²-14x+6=0
⇒4x²- 2×2x×(7/2) +(7/2)² +6 -(7/2)²
⇒(2x-7/2)²+(6- 49/4)=0
⇒(2x-7/2)²=25/4
⇒(2x-7/2)²= (5/2)²
so,
⇒(2x-7/2)=+(5/2) or, (2x-7/2)=-(5/2)
solving both equations,
2x=12/2=6
x=3
or, 2x=2/2= 1
x=1/2
so, roots are 3 and 1/2
hope you understand the whole explanation :)
multiplying whole equation by 2,we get
4x²-14x+6=0
⇒4x²- 2×2x×(7/2) +(7/2)² +6 -(7/2)²
⇒(2x-7/2)²+(6- 49/4)=0
⇒(2x-7/2)²=25/4
⇒(2x-7/2)²= (5/2)²
so,
⇒(2x-7/2)=+(5/2) or, (2x-7/2)=-(5/2)
solving both equations,
2x=12/2=6
x=3
or, 2x=2/2= 1
x=1/2
so, roots are 3 and 1/2
hope you understand the whole explanation :)
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