Question

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

Answer 1

Answer:

Option a is correct

Step-by-step explanation:

11x² - 4x = 1

Rewriting the equation:

11x² - 4x - 1 = 0

from above equation, a = 11, b = -4, c = -1

As we are asked to solve it with quadratic equation:

$x = \frac{-b +- \sqrt{b^2 - 4ac}}{2a}$

put values of a, b and c

$x = \frac{-(-4) +- \sqrt{(-4)^2 - 4(11)(-1)}}{2(11)}$

$x = \frac{4 +- \sqrt{16 + 44}}{22}$

$x = \frac{4 +- \sqrt{60}}{22}$

$x = \frac{4 +- \sqrt{15*4}}{22}$

$x = \frac{4 +- 2\sqrt{15}}{22}$

taking 2 common above and cutting it with denominator

$x = \frac{2 +- \sqrt{15}}{11}$

$x = \frac{2}{11} +- \frac {\sqrt{15}}{11}$

Answer 2

Answer:

Choice A is correct answer.

Step-by-step explanation:

We have given a quadratic equation.

11x²-4x =1

11x²-4x-1 = 0

ax²+bx+c = 0 is general quadratic equation.

Comparing above equations, we have

a  = 11 , b  = -4 and c  = -1

x = (-b±√b²-4ac) / 2a is quadratic formula to solve equation.

Putting given values in above formula, we have

x = (-(-4)±√(-4)²-4(11)(-1) ) / 2(11)

x = (4±√16+44) / 22

x = (4±√60) / 22

x = (4±√4×15) / 22

x = (4±2√15) / 22

x= 2(2±√15) / 22

x = (2±√15) / 11

x = 2/11±√15/11 is solution of given equation.