Question

Solve the quadratic equation 7x² + 9x + 2 = 0 by the quadratic formula.

Answer 1

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.