Write a quadratic equation in the form $$ x^{2}+b x+c=0 $$ that has the following r $$ \text { Roots: }-4 \pm \sqrt{10} $$ Answer

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The quadratic equation is $$ x^2 + 8x + 6 = 0 $$. To find a quadratic equation with the given roots $$ -4 \pm \sqrt{10} $$, we can use the fact that if $$ r_1 $$ and $$ r_2 $$ are the roots of the quadratic equation, then the equation can be expressed in the form: $$ x^2 - (r_1 + r_2)x + (r_1 \cdot r_2) = 0 $$ First, we identify the roots: - $$ r_1 = -4 + \sqrt{10} $$ - $$ r_2 = -4 - \sqrt{10} $$ Next, we calculate the sum of the roots $$ r_1 + r_2 $$: $$ r_1 + r_2 = (-4 + \sqrt{10}) + (-4 - \sqrt{10}) = -8 $$ Now, we calculate the product of the roots $$ r_1 \cdot r_2 $$: $$ r_1 \cdot r_2 = (-4 + \sqrt{10})(-4 - \sqrt{10}) = (-4)^2 - (\sqrt{10})^2 = 16 - 10 = 6 $$ Now we can substitute these values into the quadratic equation form: $$ x^2 - (r_1 + r_2)x + (r_1 \cdot r_2) = 0 $$ Substituting the values we found: $$ x^2 - (-8)x + 6 = 0 $$ This simplifies to: $$ x^2 + 8x + 6 = 0 $$ Thus, the quadratic equation in the form $$ x^2 + bx + c = 0 $$ is: $$ \boxed{x^2 + 8x + 6 = 0} $$

Write a quadratic equation in the form \( x^{2}+b x+c=0 \) that has the following r \[ \text { Roots: }-4 \pm \sqrt{10} \] Answer

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Write a quadratic equation in the form \( x^{2}+b x+c=0 \) that has the following r \[ \text { Roots: }-4 \pm \sqrt{10} \] Answer

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