Question

find the nature of roots of a quadratic equation 2x²-3×+5=0​

Answer 1

EXPLANATION:-

✠Given to find the nature of roots of the Quadratic equation:-

2x²-3x + 5 = 0

✠SOLUTION:-

Here we can find the nature of the roots by the discriminant . Discriminant of a Quadratic equation is b²-4ac .There are some cases to know to find the nature of roots

• If D> 0 Roots are real and distinct
• D<0 Roots are complex and conjugate
• D = 0 Roots are real and equal

2x² -3x + 5 = 0

✠Comparing with general form of Quadratic equation

ax² + bx + c = 0

• a = 2
• b = -3
• c = 5

So, Discriminant is

D = b² - 4ac

D = (-3)² -4 (2)(5)

D = 9 - 40

D = -31

So, Discriminant is less than 0 So, the roots are complex and conjugate to each other

✠Verification:-

We shall find the roots of the Quadratic equation

2x²-3x + 5 = 0

• a = 2
• b = -3
• c = 5

✠By using Quadratic formula we get ,

x = -b ± √b² -4ac/2a

x = -(-3) ±√(-3)² -4(2)(5) / 2(2)

x = 3 ± √9-40/4

x = 3 ±√-31/4

x = 3 ±√31 i/4

x = 3+√31 i / 4 (or ) 3-√31 i/4

Since , roots are not real i.e complex and also conjugate to each other

Hence verified !

Since , the roots of Quadratic equation 2x²-3x+5=0 has complex roots and conjuage to each other