How do you find the zeroes for #y=9x^2+6x-1#?

Answer 1

-0.805 or 0.138

Assuming #y=0# you can use the quadratic formula
#x=(-b±sqrt(b^2-4ac))/(2a)#
to find the roots of a quadratic. A quadratic is defined as #ax^2+bx+c# so for your case you may plug in the respective values of #a#, #b#, and #c#:
#a=9# #b=6# #c=-1#

The quadratic formula would then appear as follows:

#x=(-6±sqrt(6^2-4*9*-1))/(2*9)#
Due to the #±# sign we then have two variants for 2 answers (2 is also the degree of the polynomial which determines the amount of roots/answers of the polynomial)
#x=(-6+sqrt(6^2-4*9*-1))/(2*9)=0.138071187458# #x=(-6-sqrt(6^2-4*9*-1))/(2*9)=-0.804737854124#
I rounded the answers to #x=-0.805, x=0.138# To check your answer a graph can be utilized

graph{[-5.285, 4.58, -2.74, 2.193]} 9x^2+6x-1

:-)

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Answer 2

To find the zeroes of the quadratic equation ( y = 9x^2 + 6x - 1 ), you can use the quadratic formula ( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ), where ( a = 9 ), ( b = 6 ), and ( c = -1 ). Plugging in these values, you get:

( x = \frac{{-6 \pm \sqrt{{6^2 - 4(9)(-1)}}}}{{2(9)}} )

Simplify under the square root:

( x = \frac{{-6 \pm \sqrt{{36 + 36}}}}{{18}} ) ( x = \frac{{-6 \pm \sqrt{{72}}}}{{18}} ) ( x = \frac{{-6 \pm 6\sqrt{2}}}{{18}} ) ( x = \frac{{-1 \pm \sqrt{2}}}{{3}} )

Therefore, the zeroes of the equation are ( x = \frac{{-1 + \sqrt{2}}}{{3}} ) and ( x = \frac{{-1 - \sqrt{2}}}{{3}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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