Question

$6x {}^{2} + 39x + 162 = 0$
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Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since,it is in the form of a quadratic equation so,we here use quadratic formula to find out the roots of the given equation.

We can done in two ways either by splitting the middle term methods or directly by using through quadratic formula:

By middle term splitting method we are unable to find any factors so,it would be solve through quadratic formula.

x= -b ± √b²-4ac ÷ 2a

➝6x²+39x+162=0

a= 6,b= 39 & c= 162

➝x=-39±√ 39²-4(6)(162)/2(6)

➝x= -39±√1521-3888/12

➝x= -39±√-2367/12

➝x= -39±3√ 263i/12

Here,the discriminant b²-4ac is > 0

So,it has two real roots

➝x= -39/12 ±3√263i/12

➝x= -13/4 ±√263/12

x= -3.25+4.05i

x= -3.25+4.05ix= -3.25-4.05i

Answer 2

x= -3.25+4.05ix= -3.25-4.05i