Question

The Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, was used to solve the equation.
2x^2 − 8x + 7 = 0. Fill in the missing denominator of the solution. 4 plus or minus the square root of 2, all over blank
−16
2
4
14

Answer 1

Answer:

The correct option is  2 .

Therefore ,the missing denominator of the solution. 4 plus or minus the square root of 2, all over is  2 .

     $x=\dfrac{4\pm\sqrt{2}}{2}$

Step-by-step explanation:

For a Quadratic Equation ax² + bx + c = 0

By Formula Method we get

$x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

So we have Quadratic Equation is 2x² - 8x + 7 = 0

On Comparing we get

$a=2\\b=-8\\c=7$

Substituting a , b, c values we get

$x=\dfrac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(7)}}{2(2)}\\\\x=\dfrac{8\pm\sqrt{64-56}}{4}\\\\x=\dfrac{8\pm\sqrt{8}}{4}\\\\x=\dfrac{8\pm2\sqrt{2}}{4}\\\\x=2(\dfrac{4\pm\sqrt{2}}{4})\\\\x=\dfrac{4\pm\sqrt{2}}{2}$

Therefore ,the missing denominator of the solution. 4 plus or minus the square root of 2, all over is  2 .