1.

Find the roots of the following quadratic equations, if they exist, using the quadratic formula:(i) `3x^2-5x+2=0` (ii) `x^2+4x+5=0`(iii) `2x^2-2sqrt(2)x+1=0`

Answer» (i) `3x^2-5x+2=0`
`= 3x^2 -3x - 2x +2=0`
`= 3x(x-1)-2(x-1)=0`
`=(3x-2)(x-1)=0`
`x = 2/3 , 1 `
(ii) `x^2+4x+5=0`
`D= b^2 - 4ac = (4)^2 -(4)(1)(5)`
` = 16- 20 =-4`
`x= (-b+- sqrt D)/(2a)`
`= (-4 +- 2i)/2 = -2+-i`
(iii) `2x^2 - 2 sqrt2 x +1 = 0`
`D= b^2 - 4ac`
`= (-2 sqrt2)^2 - 4(2)(1)`
`= 8-8 = 0`
`x = -b/(2a) = -(-2 sqrt2)/(2(2)) `
`=1/sqrt2`
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