Question

find the root of the equation 3x²-2√6+2=0​

Answer 1

$\huge\red{ \frac{ \sqrt{2} }{ \sqrt{3}}}$

Step-by-step explanation:

Q.

Find the root of the equation 3x² + 2√6 + 2 = 0

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Solution -

In the standard form of quadratic equation (ax² + bx + c = 0), here

a = 3

b = -2√6

c = 2

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Using the discriminant, we will find that roots of equation are real or imaginary.

Discriminant = b² - 4ac

= (-2√6)² - 4(3)(2)

= 24 - 24

= 0

Because Discriminant = 0, so roots will be real and equal.

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Now using the formula for roots of quadratic equation -

$\frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ = \frac{ - ( - 2 \sqrt{6}) ± \sqrt{0} }{2(3)} \\ \\ = > \frac{2 \sqrt{6} }{6} \\ \\ = > \frac{ \sqrt{6} }{3} \\ \\ = > \frac{ \sqrt{2} \times \cancel{ \sqrt{3}} }{ \sqrt{3} \times \cancel{ \sqrt{3} }} \\ \\ = > \frac{ \sqrt{2} }{ \sqrt{3} }$

Hence the root of this equation is √2/√3

Note :-

If Discriminant (b² - 4ac) is,

• D > 0, roots are real and unequal
• D = 0, roots are real and equal
• D < 0, rots are unreal (imaginary)

A quadratic equation have only two zeroes

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Relation between coefficient and zeroes (roots) of equation -

Sum of zeroes = -b/a

product of zeroes = c/a

hope it helps.