Question

Factorize :
$2 {x }^{2} + x + 4$
❤(ӦｖӦ｡) First Answer Will Be Brainliest...

Answer 1

Notice, quadratic equation:x2−x+4=0x2−x+4=0 has no real roots (∵b2−4ac=−15<0∵b2−4ac=−15<0 ) hence x2−x+4x2−x+4 has no real factors.

In complex analysis, the complex factors can be obtained by applying quadratic formula to find roots of x2−x+4=0x2−x+4=0 as follows

x=−b±b2−4ac√2ax=−b±b2−4ac2a

=−(−1)±(−1)2−4(1)(4)√2(1)=−(−1)±(−1)2−4(1)(4)2(1)

=1±i15√2=1±i152

=1+i15√2,1−i15√2=1+i152,1−i152

Hence, the complex factors are as follows

x2−x+4=(x−1+i15√2)x2−x+4=(x−1+i152)(x−1−i15√2)