Question

The nature of the roots of the quadratic equation 4x^2+5x+1=0 is ..........​

Answer 1

Answer:

4x²+5x+1=0

4x²+4x+x+1=0

(4x²+4x)+(x+1)=0

4x(x+1)+1(x+1)=0

(x+1)(4x+1)=0

(x+1=0)(4x+1=0)

x=(-1), x=(-¼)

The nature of the roots is not real.

Answer 2

$\huge\underbrace{\green{\mathfrak{Solution:}}}$

Given,

Quadratic Equation ☞ 4x²+5x+1 = 0

By Factorisation

$→\;{\sf{4x²+5x+1 = 0}}$

$→\;{\sf{4x²+4x+x+1 = 0}}$

$→\;{\sf{4x(x+1)+1(x+1) = 0}}$

$→\;{\sf{(4x+1)(x+1) = 0}}$

$→\;{\sf{(4x+1) = 0\;(or)\;(x+1) = 0}}$

$→\;{\bf{x = \frac{-1}{4}, -1}}$

The Roots are ◕➜ $\fbox\red{Imaginary}$

☞ If The Roots are < 0 then they are not Equal & Imaginary.

Hope It Helps You ✌️