Question

solve the quadratic equation 8x²+2x+1=0​

Answer 1

Answer:

8x^2-2x+4x+1=0

2x(4x-1)-1(4x-1)=0

(2x-1)(4x-1)

x=1/2,1/4

Answer 2

Answer:

Roots of quadratic equation are

r = -1/8 + i√7/8 = -0.125 + 0.3307i

r =-1/8 - i√7/8 = -0.125 - 0.3307i

Step-by-step explanation:

8x^2 + 2x + 1 = 0

Let the quadratic equation be ax^2 + bx + c = 0

Value of discriminant is calculated as d =√(b^2 - 4ac)

When d > 0, then the roots are given as r = [-b ± √(b^2 - 4ac)]/2a

When d = 0, then the roots are given as r = -b/2a

When d < 0, then the roots are imaginary, r = [-b ± i√(b^2 - 4ac)]/2a

Here, a = 8, b = 2, c = 1

Discriminant is calculated

d =√(2^2 - 4×8×1) = √(4 - 32) = √-28 = 2√-7

Here, d < 0

Thus, roots are imaginary

Roots are calculated as

r = [-b ± √(b^2 - 4ac)]/2a

r = (-2 ± i2√7)/(2×8)

r = 2(-1 ± i√7)/(2×8)

r = (-1 ± i√7)/8

Roots are

r = -1/8 + i√7/8 = -0.125 + 0.3307i

r =-1/8 - i√7/8 = -0.125 - 0.3307i