-√3, 3√3 Write a quadratic equation in the variable X having the given numbers as solutions. Type in standard form ax^2 + bx +c =0
a x ^ 2 + b x + c = a ( x - x1 ) ( x - x2 )
In this case :
x 1 = sq
a x ^ 2 + b x + c = a ( x - x1 ) ( x - x2 )
a leading coefficient
x1 and x2 roots
In this case :
x 1 = - sqrt ( 3)
x 2 = 3 sqrt ( 3 )
a x ^ 2 + b x + c = a [ ( x - ( - sqrt ( 3 ) ) ] * [ ( x - 3 sqrt ( 3 ) ) =
a [ ( x + sqrt ( 3 ) ) ] * [ ( x - 3 sqrt ( 3 ) ) =
a [ x * x + x * sqrt ( 3 ) - 3 sqrt ( 3 ) * x - 3 * sqrt ( 3 ) * sqrt ( 3 ) ] =
a [ x ^ 2 - 2 sqrt ( 3 ) x - 3 * 3 ] =
a [ x ^ 2 - 2 sqrt ( 3 ) x - 9 ]
a [ x ^ 2 - 2 sqrt ( 3 ) x - 9 ] = 0 Divide both sides by a
x ^ 2 - 2 sqrt ( 3 ) x - 9 = 0 / a
x ^ 2 - 2 sqrt ( 3 ) x - 9 = 0
To write a quadratic equation with the given solutions, we can use the fact that the solutions of a quadratic equation in the form ax^2 + bx + c = 0 are equal to the roots of the equation.
Given solutions are -√3 and 3√3.
Since these are the solutions, their equations would be:
(x - (-√3))(x - (3√3)) = 0
Let's simplify this equation:
(x + √3)(x - 3√3) = 0
Expanding the equation:
x^2 - 3√3x + √3x - 9√9 = 0
Combining like terms:
x^2 - 2√3x - 9√3 = 0
Therefore, the quadratic equation in standard form is:
x^2 - 2√3x - 9√3 = 0