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MrMuchimi
3 years ago
9

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 =
Mathematics
2 answers:
finlep [7]3 years ago
9 0

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.

balandron [24]3 years ago
5 0
          ____________
2 +- <span>√-2^2 - 4(-3)(6) )
------------------------------
              2(-3)</span>
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