There are 9 balloons remaining, of which 4 are yellow. therefore the probability that the next balloon is also yellow is 4/9
<span>The roots of a quadratic equation ax²+bx+c=0 can be determined by calculating the discriminant Δ=b²-4ac.
If Δ>0, there are two distinct real solutions.
If Δ=0, there is one real solution.
If Δ<0, there are no real solutions and two complex solutions.
![3x^2+12x-3=0 \\ \\ a=3 \\ b=12 \\ c=-3 \\ \\ \Delta=b^2-4ac=12^2-4 \times 3 \times (-3)=144+36=180](https://tex.z-dn.net/?f=3x%5E2%2B12x-3%3D0%20%5C%5C%20%5C%5C%0Aa%3D3%20%5C%5C%20b%3D12%20%5C%5C%20c%3D-3%20%5C%5C%20%5C%5C%0A%5CDelta%3Db%5E2-4ac%3D12%5E2-4%20%5Ctimes%203%20%5Ctimes%20%28-3%29%3D144%2B36%3D180)
Δ>0, so there are two distinct real solutions. The answer is A.
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Answer:
see explanation
Step-by-step explanation:
Given
6x² + x - 1 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 1 = - 6 and sum = + 1
The factors are + 3 and - 2
Use these factors to split the x- term
6x² + 3x - 2x - 1 = 0 ( factor the first/second and third/fourth terms )
3x(2x + 1) - 1(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(3x - 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)