Question

write the discriminant of the quadratic equation 3x2 -2root6+2=0​

Answer 1

Question

Write the discriminant of the quadratic equation 3x2 -2√6+2=0.

Answer

3x² -2√6+2=0

Let,

a = 3

b = -2√6

c = 2

We have,

Discriminant = b² - 4ac

= -2√6 - 4 × 3 × 2

= 24 - 24

= 0

Therefore, the discriminant is O

Since the value is zero, the nature of roots are real equal and rational.

Must Know

Must Knowb²-4ac = 0 → The roots are real, equal and rational

b² - 4ac > O also a perfect square → The roots are real, distinct and rational

b² - 4ac > O but not a perfect square → The roots are real, distinct and irrational

roots are real, distinct and irrationalb²-4ac < 0 → The roots are imaginary

The roots are imaginaryb²- 4ac >/= O → The roots are real.

A function of coefficients of polynomial (quadratic) equation where it's value value gives us information about the roots of the polynomial is called determinants

Answer 2

${\huge{\rm{\underline{\underline{\maltese\; Question:-}}}}}$

Q) Write the Discriminant of the Quadratic Equation -

3x² - 2√6x + 2 = 0 .

${\huge{\underline{\underline{\rm{\maltese\;Answer\checkmark}}}}}$

☆ Given :-

• Equation → 3x² - 2√6x + 2 = 0

☆ To Find :-

• Discriminant of the Equation .

☆ Solution :-

The standard Quadratic Equation is in the form -

$\boxed{ \tt{a {x}^{2} + bx + c = 0}}$

Compare it with the given Equation ; we get -

• a = 3
• b = -2√6
• c = 2

Using the Formula to find Discriminant -

$\mapsto \rm \: d = {b}^{2} - 4ac$

$\mapsto \rm \: d = {( - 2 \sqrt{6} )}^{2} - 4 \times 3 \times 2$

$\mapsto \rm \: d = ( - 2 \sqrt{6} \times - 2 \sqrt{6} ) - 24$

$\mapsto \rm \: d = 24 - 24$

$\mapsto \boxed{ \pink{ \rm \: d = 0 \: }}$

So ,

The Discriminant of the given Equation would be Zero ( 0 ) .

_________________________

☆ Know More :-

• If ,

$\tt \: d > 0 \: \: \: roots \: are \: real \: and \: distinct$

• If ,

$\tt \: d = 0 \: \: \: roots \: are \: real \: and \: equal.$

• If ,

$\tt \: d < 0 \: \: \: roots \: are \: imaginary \: .$

• The degree of a Quadratic Equation is 2 .

• A Quadratic Equation has 2 roots .