Find roots of the quadratic equation root 3x2+10x+7root3=0
Answers
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Given,
√3x² + 10x + 7√3 = 0.
To find,
The roots of the quadratic equation.
Solution,
The roots of the quadratic equation √3x² + 10x + 7√3 = 0 will be -√3 and -7/√3.
We can easily solve this problem y following the given steps.
Now, we can find its roots by splitting the middle term into two terms such that their multiplication will be (√3x² × 7√3) and the sum will be 10x. So, these two terms will be 7x and 3x.
According to the question,
√3x² + 10x + 7√3 = 0
√3x² + 3x + 7x + 7√3 = 0
√3x (x + √3) + 7 (x + √3) = 0 [Taking √3x common from the first two terms and 7 common from the last two terms.]
(x + √3) (√3x + 7) = 0 [ Taking (x + √3) common.]
Equating both the brackets with zero,
x + √3 = 0 and √3x + 7 = 0
x = -√3 and x = -7/√3 ( Moving 7 from the left-hand side to the right-hand side will result in the change of the sign from plus to minus.)
Hence, the roots of the quadratic equation √3x² + 10x + 7√3 = 0 are -√3 and -7/√3.