1.

Solve the following quadratic equations by factorisation : (i) 4-11x=3x^(2) (ii) x^(2)-(11)/(4)x+(15)/(8)=0

Answer»

SOLUTION :(i) Given EQUATION is
`4-11x=3x^(2)`
`implies3x^(2)+11x-4=0`
`implies3x^(2)+(12-1)X-4=0`
`implies3x^(2)+12x-x-4=0`
`implies3x(x+4)-1(x+4)=0`
`IMPLIES(3x-1)(x+4)=0`
`implies3x-1=0orx+4=0`
when `3x-1=0impliesx=(1)/(3)`
and `x+4=0impliesx=-4`
Hence, `(1)/(3)and-4` are roots of equation.
(ii) Given equation is
`x^(2)-(11)/(4)x+(15)/(8)=0`
Multiplying both sides by 8, we get
`8x^(2)-22x+15=0`
`implies8x^(2)-(12+10)x+15=0`
`implies8x^(2)-12-10x+15=0`
`implies4x(2x-3)-5(2x-3)=0`
`implies(2x-3)(4x-5)=0`
:. either `2x-3=0or4x-5=0`
`implies2x=3or4x=5`
`impliesx=(3)/(2)orx=(5)/(4)`
Hence, `(3)/(2)and(5)/(4)` are the roots of given equation.


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