Question

Solve the following quadratic equation using formula:

x² + 10x + 2 = 0

Answer 1

x² + 10x + 2 = 0, comparing with ax² + bx + c = 0

We get, a = 1, b = 10, c = 2

∴ b² – 4ac = (10)² – 4 × 1 × 2

= 100 – 8

= 92

∵ x = `(-b +- sqrt(b^2 - 4ac))/(2a)`

∴ x = `(-10 +- sqrt(92))/(2 xx 1)`

∴ x = `(-10 +- sqrt(23 xx 4))/2`

∴ x = `(-10 +- 2sqrt(23))/2`

∴ x = `(2(-5 +- sqrt(23)))/2`

∴ x = `-5 + sqrt(23)` or x = `- 5 - sqrt(23)`

∴ Roots of the quadratic equation are `-5 + sqrt(23)` or `-5 - sqrt(23)`