Question

42.
The discriminate of the equation 3x2 – 2v3x +1 = 0 is​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore D=0}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies {3x}^{2} - 2 \sqrt{3} x + 1 = 0 \\ \\ \underline \bold{To \: Find : } \\ \implies d = ?$

• According to given question :

$\bold{a = 3 \: \: \: \: b = - 2 \sqrt{3} \: \: \: \: c =1 } \\ \\ \bold{Using \: formula \: of \: discriminant : } \\ \implies d = {b}^{2} - 4ac \\ \\ \bold{Putting \: given \: values : } \\ \implies d = ({ - 2 \sqrt{3} })^{2} - 4 \times 3 \times 1 \\ \\ \implies d = 4 \times 3 - 12 \\ \\ \implies d = \cancel{12 }\cancel{ - 12} \\ \\ \bold {\implies d = 0} \\ \\ \bold{For \: zeroes : } \\ \implies x = \frac{ - b \pm \sqrt{d} }{2a} \\ \\ \implies x = \frac{ - ( - 2 \sqrt{3} ) \pm \sqrt{0} }{2 \times 3} \\ \\ \implies x = \frac{2 \sqrt{3} }{6} \\ \\ \bold{\implies x = \frac{ \sqrt{3} }{3} }$

Answer 2

SOLUTION:-

Given:

The discriminate of the equation;

•3x² - 2√3x + 1=0

Therefore,

Compare the given equation with;

⚫Ax² + Bx + C= 0

•A= 3

•B= -2√3

•C= 1

We know that,

D= b² - 4ac is called discriminant.

So,

=) D= (2√3)² - 4(3)(1)

=) D= 4×3 - 4× 3

=) D= 12 - 12

=) D= 0

Thus,

•The roots of the equation are real & equal.

&

In this case:

$= > \frac{ - b ± 0}{2a} \\ \\ = > \frac{ - b}{2a}$

Some related formulas:

•If b² -4ac= D≥0, then roots are real.

•If b² - 4ac > 0, then roots are real & unequal.

Hope it helps ☺️