Question

Find the roots of the following quadratic equations by factorisation:
(i) `x^2-3x-10=0`
(ii) `2x^2-x-6=0`
(iii) `sqrt(2)x^2+7x+5sqrt(2)=0`
(iv) `100 x^2-20 x+1=0`
(v) `100 x^2-20 x+1=0`

Answer 1

(i) `x^2 - 3x -10=0`
= `x^2 -5x +2x-10=0`
`= x(x-5)+2(x-5)=0`
`=(x-5)(x+2)=0`
`x=5,-2`
(ii) `2x^2 +x-6=0`
`2x^2 + 4x -3x -6=0`
`2x(x+2)-3(x+2)=0`
`(2x-3)(x+2)=0`
`x=3/2, -2`
(iii)`sqrt2 x^2 +7x +5sqrt2= 0`
`sqrt2x^2 +5x+2x +5sqrt2 = 0`
`x(sqrt2x +5) + sqrt2(sqrt2 x +5)`
`(x+ sqrt2)(sqrt2x+5) = 0`
`x= -sqrt2, -5/sqrt2`
(iv) `2x^2 -x +1/8=0`
`16x^2 - 8x +1=0`
`16x^2 - 4x -4x +1=0`
`4x(4x-1)-1(4x-1)=0`
`(4x-1)(4x-1)`
`x=1/4,1/4`
(v) `100x^2 - 20x +1=0`
`100x^2 - 10x -10x +1=0`
`10x(10x -1) -1(10x-1) = 0`
`(10x-1)(10x-1)`
`x=1/10,1/10`
answer