Question

Solve the following quadratic equations by formula method.

5m² – 4m – 2 = 0

Answer 1

5m² – 4m – 2 = 0

Comparing the above equation with am² + bm + c = 0, we get

a = 5, b = – 4, c = – 2

∴ b² – 4ac = (– 4)² − 4 × 5 × (– 2)

= 16 + 40

= 56

m = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`

= `((-4) +- sqrt(56))/(2(5))`

= `(4 +- sqrt(4 xx 14))/10`

= `(4 +- 2sqrt(14))/10`

= `(2(2 +- sqrt(14)))/10`

∴ m = `(2 +- sqrt(14))/5`

∴ m = `(2 + sqrt(14))/5` or m = `(2 - sqrt(14))/5`

∴ The roots of the given quadratic equation are `(2 + sqrt(14))/5` and `(2 - sqrt(14))/5`