Question

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What are the exact solutions of x2 − 3x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a? x = the quantity of 3 plus or minus the square root of 37 all over 2 x = the quantity of negative 3 plus or minus the square root of 37 all over 2 x = the quantity of 3 plus or minus the square root of 19 all over 2 x = the quantity of negative 3 plus or minus the square root of 19 all over 2

Answer 1

Answer:

x = the quantity of 3 plus or minus the square root of 37 all over 2

Step-by-step explanation:

Given/To Find:

What are the exact solutions of x2 − 3x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a?

Answer choices:

x = the quantity of 3 plus or minus the square root of 37 all over 2

x = the quantity of negative 3 plus or minus the square root of 37 all over 2 x = the quantity of 3 plus or minus the square root of 19 all over 2

x = the quantity of negative 3 plus or minus the square root of 19 all over 2

Solve:

By using the quadratic formula, the solutions are

$x=\frac{-(-3)±\sqrt{(-3)^2-4\times1\times(-7)}}{2\times1}$

$x=\frac{3±\sqrt{37}}{2}$

Hence, the answer is :

x = the quantity of 3 plus or minus the square root of 37 all over 2

Kavinsky

Answer 2

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:

$x^2 - 3x - 7 = 0$

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:

$ax^2+bx+c=0$

is solved by using the formula:

$x=\frac{-b±\sqrt{x} b^2-4ac}{2a}$

Here we have:

a=1, b=-3 and c=-7.

Hence, the solution of the equation is:

$x=\frac{-(-3)±\sqrt{(-3)^2-4*(-7)*1} }{2*1}$

$x=\frac{3±\sqrt{9+28} }{2}$

$x=\frac{3±\sqrt{37} }{2}$

Hence, the solution is:

x = the quantity of 3 plus or minus the square root of 37 all over 2

( i.e.

$x=\frac{3±\sqrt{37} }{2}$ )