Question

what is the natute of root of the equation 5x²-2x-3=0​

Answer 1

Answer:

real and distinct roots

Step-by-step explanation:

5x²-2x-3 = o

a=5 b= -2 c = -3

formula

b²- 4ac

(-2)² - ( 4×5×-3)

4 +60

64

0<64

Answer 2

Answer:

Step-by-step explanation:

Given,

$\sf 5x^2 - 2x - 3 = 0$

To Find :-

Nature of the roots

Solution :-

To Find the Nature of the roots , First we need to fine the value of Discriminant(D).

D = Discriminant = $\sf b^2-4ac$

Comparing " 5x^2 - 2x - 3 = 0 " with general form of quadratic equation " ax^2 + bx + c = 0" :-

a = 5 , b = - 2 , c = - 3

D = $\sf b^2-4ac$

= $\sf (-2)^2-4(5)(-3)$

= $\sf 4 + 60$

= 64

D = 64 > 0

We know that :-

If D > 0 and 'D' is a perfect square then the roots are rational and distinct.

as D = 64 > 0 and '64' is also a perfect square the nature of the roots are rational and distinct.

Know More :-

If a , b , c are real numbers

1) If D > 0 , then the roots are real and distinct.

2) If D = 0, then the roots are real and equal.

3) If D < 0 , then  the roots are complex and conjugate to each other

If a , b , c are rational numbers

1) If D > 0 and 'D' is a perfect square then the roots are rational and distinct.

2) If D > 0 and 'D' not  is a perfect square then the roots are irrational and conjugate to each other.

3) If D = 0 , then the roots are rational and equal.

4) If D < o , then the roots are not real and complex and conjugate to each other.