12x² + 2x - 4 = 0 is the equation?

Question

Find the value of the discriminant and describe the nature of the roots of each quadratic equation. Then solve the equation. Express irrational roots as exact and approximate to the nearest hundredth

Answer 1

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d = 2^2 - 4(12)(-4) = 4 + 192 = 196

There are two real roots, since d > 0.

12x^2 + 2x - 4 = 0

(4x - 2)(3x + 2) = 0

4x - 2 = 0 or 3x + 2 = 0

x = 0.5 or x = -0.67

Answer 2

Discriminant = b2 - 4ac = 196 > 0 so real roots...

12x2 + 2x - 4 = 12x2 + 8x - 6x - 4

= (4x - 2)(3x + 2)

roots are 1/2 and -2/3