Question

1) Determine the nature of the roots for the quadratic equation
$\sqrt{3 {x }^{2} } + \sqrt{2x} - 2 \sqrt{3 } = 0$
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Answer 1

Given :-

√3 x² + √2 x - 2√3 = 0

To find :-

The nature of the roots of the equation.

Solution :-

Given quardratic equation is

√3 x² + √2 x - 2√3 = 0

On comparing with the standard quadratic equation ax²+bx+c = 0

a = √3

b = √2

c = -2√3

To know the nature of the roots of the equation we have to find the value of the discriminant.

The discriminant of ax²+bx+c = 0 is D = b²-4ac

The discriminant of the given equation

=> D = (√2)²-4(√3)(-2√3)

=> D = 2-(-24)

=> D = 2+24

=> D = 26

=> D > 0

The roots are distinct and real.

Answer :-

Nature of the roots : The roots are distinct and real.

Points to know :-

♦ The standard quadratic equation is

ax²+bx+c = 0

♦ The discriminant of ax²+bx+c = 0 is D = b²-4ac

♦ If D > 0 then the roots are distinct and real.

♦ If D = 0 then the roots are equal and real.

♦ If D < 0 then the roots are imaginary (No real).

Answer 2

Answer:

Real and unequal

Step-by-step explanation:

3x^2 +2x -2 =0

comparing with ax^2 + bx + c = 0

a= 3 , b = 2 , c = -2

Nature of root depends on b^2 - 4ac

b^2 - 4 ac= ( 2)^2 - ( 4×3× -2)

= 4 +24

= 28

b^2 - 4 ac > 0 which is positive

therefore nature of root is real and unequal