Question

Determine the nature of the roots of the
the quadratic equation 2x ² - 5x + 3=0​

Answer 1

Step-by-step explanation:

(2x)²-5x+3 =0

4x-5x+3=0

1x+3=0

x=0-3

x=0

Answer 2

Given :-

• quadratic equation - 2x ² - 5x + 3=0

To find:-

• Nature of roots

solution :-

=> we have 2x ² - 5x + 3=0

=> here ,

• a= 2
• b= -5
• c=3

Discriminant (D)=b ² - 4ac

=> put value

=> (-5)²-4(2)(3)

=>25- 24

=> 1

=> 1 > 0

=> since D>0 ,the equation has real roots

Concept : Nature of roots

Let the quadratic equation be ax²+bx+c=0

Then ,

x=-b±√b² - 4ac

2a

so , a quadratic equation ax²+bx+c=0

1) has no real roots if b²-4ac<0

2) has two equal roots if b² -4ac =0

3) has two distinct roots if b² -4ac> 0

4) has real roots if b²- 4ac ≥ 0

Note: Discriminant b²- 4ac is denoted by D .

Thanks

Hope it's helpful