Question

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x =

Answer 1

Answer:

$x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$ shows correct substitution of the values a, b, and c  from the given quadratic equation  $-3x^2-2x+6=0$  into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation $-3x^2-2x+6=0$

We have to show the correct substitution of the values a, b, and c from the given quadratic equation  $-3x^2-2x+6=0$  into quadratic formula.

The standard form of quadratic equation is $ax^2+bx+c=0$ then the solution of quadratic equation using quadratic formula is given as $x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Consider the given  quadratic equation $-3x^2-2x+6=0$

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

$x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$

Simplify, we have,

$x_{1,2}=\frac{2\pm\sqrt{76} }{-6}$

Thus, $x_{1}=\frac{2+\sqrt{76} }{-6}$ and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

$x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}$

Thus, $x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$ shows correct substitution of the values a, b, and c  from the given quadratic equation  $-3x^2-2x+6=0$  into quadratic formula.

Answer 2

          ____________
2 +- √-2^2 - 4(-3)(6) )
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              2(-3)