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Question
Solve the following quadratic equations by formula method.
5m2 – 4m – 2 = 0
Solution
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`
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