Question

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

Answer 1

Choice A is correct answer.

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.

Answer 2

Option a is correct

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 = (-b +- √(b^2 - 4ac))/(2a)`

put values of a, b and c

`x = (-(-4) +- √((-4)^2 - 4(11)(-1)))/(2(11))`

`x = (4 +- √(16 + 44))/(22)`

`x = (4 +- √(60))/(22)`

`x = (4 +- √(15*4))/(22)`

`x = (4 +- 2√(15))/(22)`

taking 2 common above and cutting it with denominator

`x = (2 +- √(15))/(11)`

`x = (2)/(11) +- \frac {√(15)}{11}`