Find the Roots of the Quadratic Equation 3x2−7x−6=0

بواسطة admin - يناير 18, 2022

Find the roots of the quadratic equation 3`x^2` − 7`x` − 6 = 0.

Given,

3`x^2` - 7`x` - 6 = 0

Comparing with `ax^2` - `bx` + `c` = 0

So, a = 3, b = -7 and c = -6

We Know that,

D = `"b"^2` - 4ac

⇒ D = `(-7)^2` - 4`\times`3`\times` (-6)

⇒ D = 49 + 72

⇒ D = 121

So, the root of the equation is given by

⇒ x = `\frac{-b\pm\sqrt{D}}{2a}`

⇒ x = `\frac{-(-7)\pm\sqrt{121}}{2\times3}`

⇒ x = `\frac{7\pm11}{2\times6}`

Now,

⇒ x = `"7 + 11"/6″`

⇒ x = `18/6`

⇒ x = 3

⇒ x = `"7 – 11"/6`

⇒ x = `-4/6`

⇒ x = `-2/3`

Hence, the roots of the equation (3`x^2` - 7`x` - 6 = 0) are 3 and `-2/3`.

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