Question

what is the nature of the roots of the quadratic equation:2x^2-5x+3=0​

Answer 1

Answer:

Nature of roots are of three types:

• Real and distinct roots ( When D > 0 )
• Real and equal roots ( When D = 0 )
• Unreal or imaginary roots ( When D < 0 )

The above set of roots can be found from a quadratic equation based on useful tool called Discriminant, denoted with letter 'D'.

Discriminant is a value which is determined by the coefficients of a given quadratic equation.

D = b² - 4ac

• a is the coefficient of x²
• b is coefficient of x
• c is the constant

According to the question, Eqn: 2x² - 5x + 3 = 0

• a = 2
• b = -5
• c = 3

→ D = (-5)² - 4(2)(3)

→ D = 25 - 24 = 1

Since the D value is greater than zero ( 1 ), it would have real and distinct roots.

Answer 2

Question :---- what is the nature of the roots of the quadratic equation:2x^2-5x+3=0 ?

Concept used :----

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by;

D = B^2 - 4•A•C

• If D = 0 , then the given quadratic equation has real and equal roots.

• If D > 0 , then the given quadratic equation has real and distinct roots.

• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...

_____________________________

Solution :---

Given Equation is 2x² - 5x + 3 = 0 .

Comparing it with A•x^2 + B•x + C = 0 we get,

→ A = 2

→ B = (-5)

→ C = 3 .

Now, lets check discriminant of the Equation :--

→ D = B^2 - 4•A•C

→ D = (-5)² - 4 * 2 * 3

→ D = 25 - 24

→ D = 1 .

➥ we get D > 0

Hence, if D > 0 then the given quadratic equation has real and distinct roots.