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Question

Solve the following quadratic equations by factorization method :

(i) x2+10ix21=0

(ii) x2+(12i)x2i=0

(iii) x2(23+3i)x+63i=0

(iv)6x217ix12=0


Solution

(i) x2+10ix21=0x2+10ix+21i2=0               [i2=1]x2+7ix+3ix+21i2=0x(x+7i)+3i(x+7i)=0(x+3i)(x+7i)=0x=3i,7i

(ii) x2+(12i)x2i=0x2+x2i2i=0x(x+1)2i(x+1)=0(x2i)(x+1)=0x=2i,1 (iii) x2(23+3i)x+63i=0x223x3ix+63i=0x(x23)3i(x23)=0(x3i)(x23)=0x=3i,23

(iv)6x217ix12=06x217ix12=0                      [i2=1]6x29ix8ix+12i2=03x(2x3i)4i(2i3i)=0(3x4i)(2x3i)=0x=43i  Or  32i

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