Q. 14.3( 296 Votes )

Find the roots of the following quadratic equations by factorisation:

(i)

(ii)

(iii)

(iv)

(v)

Answer :

(i) X2 – 3x – 10


= x2 – 5x +2x – 10


= x(x – 5 ) + 2(x – 5 )


= (x – 5 )(x+2)


Roots of this equation are the values for which (x – 5 )(x+2) = 0


x - 5 = 0 or x + 2 = 0

i.e.,

x = 5 or x = -2


(ii) 2 x2 + x – 6


= 2x2 + 4x – 3x – 6


= 2x (x+2) – 3(x+2)


= (x+2)(2x – 3 )


Roots of this equation are the values for which (x+2)(2x – 3) = 0


x+ 2= 0 or 2x – 3 = 0


x = −2 or x =


(iii)





Roots of this equation are the values for which = 0


= 0 or = 0



(iv)






Roots of this equation are the values for which (4x – 1 )2 = 0


Therefore,


(4x – 1 ) = 0 or (4x – 1) = 0


i.e.,


(v) 100x2 – 20x +1


= 100x2 – 10x – 10x +1


=10x(10x – 1) – 1 (10x – 1)


=(10x – 1)2


Roots of this equation are the values for which (10x – 1)2 = 0


Therefore,


(10x – 1) = 0 or (10x – 1) = 0


i.e.,

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