Question

The nature of roots of the quadratic equation 4x2+5x+1=0 is​

Answer 1

Step-by-step explanation:

$4 {x}^{2} + 5x + 1 = 0 \\ 4 {x}^{2} + 4x + 1x + 1 = 0 \\ 4x(x + 1) + 1(x + 1) = 0 \\ (4x + 1)(x + 1) \\ 4x + 1 = 0 \\ 4x = - 1 \\ x = \frac{ - 1}{4} \\ \\ x + 1 = 0 \\ x = - 1$

I hope it helps you

Answer 2

Step-by-step explanation:

Given quadratic equation is: 4x2 5x-1 = 0

Comparing the above equation with ax2 + bx + c = 0,

We get a = 4, b = -5 and c = -1

Now, b2-4ac = (-5)² - 4(4)(−1)

= 25+ 16

= 41 > 0

Hence, roots of the quadratic equation are real and distinct.