Respuesta :
Answer:
(a) x = the quantity of 3 plus or minus the square root of 37 all over 2
[tex]x=\dfrac{3\pm\sqrt{37}}{2}[/tex]
Step-by-step explanation:
The given equation is a second-degree (quadratic) equation. Its solutions can be found using the "quadratic formula" applicable to such equations.
Quadratic formula
A quadratic equation written in standard form is ...
[tex]ax^2+bx+c=0[/tex]
Its solutions are given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Application
Comparing the given quadratic to the standard form, we see the coefficients are ...
a = 1, b = -3, c = -7
Using these values in the quadratic formula gives the solutions as ...
[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-7)}}{2(1)}=\dfrac{3\pm\sqrt{9+28}}{2}\\\\\boxed{x=\dfrac{3\pm\sqrt{37}}{2}}[/tex]
The verbal description of this expression matches the first choice.
Answer:
The exact solution is:
x = the quantity of 3 plus or minus the square root of 37 all over 2
Step-by-step explanation:
We are asked to find the exact solution of the polynomial equation which is given by:
[tex]x^2-3x-7=0[/tex]
We know that the solution of the equation are the possible value of x which is obtained on solving the equation and hence satisfy the equation.
Now, on solving the quadratic equation i.e. degree 2 polynomial equation using the quadratic formula:
That is any polynomial equation of the type:
[tex]ax^2+bx+c=0[/tex]
is solved by using the formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
a=1, b=-3 and c=-7.
Hence, the solution of the equation is:
[tex]x=\dfrac{-(-3)\pm \sqrt{(-3)^2-4\times (-7)\times 1}}{2\times 1}\\\\\\x=\dfrac{3\pm \sqrt{9+28}}{2}\\\\\\x=\dfrac{3\pm \sqrt{37}}{2}[/tex]
Hence, the solution is:
x = the quantity of 3 plus or minus the square root of 37 all over 2
( i.e.
[tex]x=\dfrac{3\pm \sqrt{37}}{2}[/tex] )
