Question

Find the roots of quadratic equation: 3x2 - 7x - 6 = 0​

Answer 1

Answer:

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Answer 2

Given,

A quadratic  equation 3x²-7x-6

To find,

The factors of the equation

Solution,

The equation is of the form of ax²+bx+c where a = 3, b = -7 and c = -6.

First, we need to find the discriminant of the equation.

⇒   D = b²-4ac

⇒   D = (-7)² - 4(3)(-6)

⇒   D = 49 + 72

⇒   D = 121

Since D = 121 the equation must have roots.

$x=\frac{-b+\sqrt[]{D} }{2a}$ and $x=\frac{-b-\sqrt[]{D} }{2a}$

First root,

⇒  x = (-(-7) +√121)/2(3)

⇒  x = (7 + 11)/2(3)

⇒  x = 18/6

⇒  x = 3

Second root,

⇒  x = (-(-7) -√121)/2(3)

⇒  x = (7 - 11)/2(3)

⇒  x = -4/6

⇒  x = -2/3.

Hence, the roots of the equation  3x²-7x-6 are x = 3 and x = -2/3.