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Question
Solve the quadratic equation 7x2 + 9x + 2 = 0 by the quadratic formula.
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Solution
The given equation is 7x2 + 9x + 2 = 0
On comparing the given quadratic equation with ax2 + bx + c = 0, we get
a = 7, b = 9, c = 2
Now, using the quadratic formula,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
⇒ x = `(-9 +- sqrt((9)^2 - 4(7)(2)))/(2(7))`
= `(-9 +- sqrt(81 - 56))/14`
= `(-9 +- sqrt(25))/14`
⇒ x = `(-9 + sqrt(25))/14` or x = `(-9 - sqrt(25))/14`
⇒ x = `(-9 + 5)/4` or x = `(-9 - 5)/14`
⇒ x = `(-4)/14` or x = `(-14)/14`
⇒ x = `(-2)/7` or x = – 1.
As a result, the two roots of the above quadratic equation are `- 2/7` and – 1.
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