Find the x-intercepts (if any) for the graph of the quadratic function.? 6x^2 +12x+5=0

Give your answers in exact form. Show your work

2 Answers
Mar 22, 2018

Just apply the formula x=(-b(+)or(-)(b^2-4*a*c)^(1/2))/(2*a)
where the quadratic function is a*x^2+b*x+c=0

Explanation:

In your case:
a=6
b=12
c=5
x_(1)=(-12+(12^2-4*6*5)^(1/2))/(2*6)=-0.59
x_2=(-12-(12^2-4*6*5)^(1/2))/(2*6)=-1.40

Mar 22, 2018

-0.5917 and -1.408

Explanation:

The x intercepts are basically the points where the line touches the x-axis. On the x-axis, the y co-ordinate is always zero so now we find values of x for which 6x^2 +12x + 5 = 0.

This is a quadratic equation and we can solve this using the quadratic formula:
x = (-b+-sqrt(b^2-4*a*c))/(2*a)

Now, for 6x^2+12x+5,
a=6. b=12, c=5.
On substituting the values in the formula, we get

x= (-12+-sqrt(12^2-4*6*5))/(2*6)

= (-12+-sqrt(144-120))/(12)

= (-12+-sqrt(24))/(12)

This gives us the two values as -0.5917 and -1.408

Hence the two x intercepts for the given equation are -0.5917 and -1.408.