How do you solve the quadratic using the quadratic formula given 3x2−11x=8−14x over the set of complex numbers?

1 Answer
Shwetank Mauria
Aug 30, 2016

Solution is −12−√1056 and −12+√1056

Explanation:

For the equation ax2+bx+c=0, the roots are given by x=−b±√b2−4ac2a. As can be seen type of roots depend upon discriminant b2−4ac. If it is negative, roots are complex and if it is a complete square (and coefficients are rational), roots are rational.

In the equation 3x2−11x=8−14x or 3x2+3x−8=0, the discriminant is (3)2−4×3×(−8)=9+96=105, which is not a complete square and hence roots are irrational (not complex as mentioned in question).

Roots are x=−3±√1052×3

= −3±√1056

= −12±√1056

Hence solution is −12−√1056 and −12+√1056.

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