Question

Use the quadratic formula to solve 9x^2+6x-17=0

A.X=-1,-5
B.X=-1+3√2 /3
C.X=3+√14 /10
D.X=-6+√31 /2

Answer 1

option (b) is correct.

`x_1=(-1+3√(2))/(3),\:x_2=-(1+3√(2))/(3)`

Explanation:

Given equation
`9x^2+6x-17=0`

We have to solve the given quadratic equation using quadratic formula.

For the given standard quadratic equation
`ax^2+bx+c=0`

Quadratic formula is given as
`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

Comparing with given quadratic equation, we have a = 9, b = 6 and c = -17

Substitute in quadratic formula, we have,

`x_(1,\:2)=(-6\pm √(6^2-4\cdot \:9\left(-17\right)))/(2\cdot \:9)`

Simplify , we have
`√(6^2+4\cdot \:9\cdot \:17)=√(648)`

we get,

`x_(1,\:2)=(-6\pm√(648))/(2\cdot \:9)`

Also,
`√(648) =√(3^4\cdot \:2^3)=18√(2)`

we have,

`x_(1,\:2)=(-6\pm 18√(2))/(2\cdot \:9)`

Thus, seperating both facotors, we have,

`x_(1)=(-6\+18√(2))/(2\cdot \:9)` and
`x_(2)=(-6\-18√(2))/(2\cdot \:9)`

Simplify, both we get,

`x_1=(-1+3√(2))/(3),\:x_2=-(1+3√(2))/(3)`

Thus, option (b) is correct.