Solve the quadratic equations by factorization method only:21x2 + 9x

1.	Solve the quadratic equations by factorization method only:21x2 + 9x + 1 = 0
Answer» Given as 21x² + 9x + 1 = 0 Now we shall apply discriminant rule, Where, x = (-b ± √(b² – 4ac))/2a Since, a = 21, b = 9, c = 1 Therefore, x = (-9 ± √(9² – 4 (21)(1)))/ 2(21) = (-9 ± √(81 - 84))/42 = (-9 ± √(-3))/42 = (-9 ± √3(-1))/42 Then we have i² = –1 On substituting –1 = i² in the above equation, we get x = (-9 ± √3i²)/42 = (-9 ± √(√3i)²/42 = (-9 ± √3i)/42 = -9/42 ± √3i/42 = -3/14 ± √3i/42 ∴ The roots of the given equation are -3/14 ± √3i/42

Solve the quadratic equations by factorization method only:21x2 + 9x + 1 = 0

Answer»

Given as 21x² + 9x + 1 = 0

Now we shall apply discriminant rule,

Where, x = (-b ± √(b² – 4ac))/2a

Since, a = 21, b = 9, c = 1

Therefore,

x = (-9 ± √(9² – 4 (21)(1)))/ 2(21)

= (-9 ± √(81 - 84))/42

= (-9 ± √(-3))/42

= (-9 ± √3(-1))/42

Then we have i² = –1

On substituting –1 = i² in the above equation, we get

x = (-9 ± √3i²)/42

= (-9 ± √(√3i)²/42

= (-9 ± √3i)/42

= -9/42 ± √3i/42

= -3/14 ± √3i/42

∴ The roots of the given equation are -3/14 ± √3i/42