Mattie uses the discriminamt to determine the number of zeros the quadratic equation 0=3x^2-7x+4?

There are 2 roots for this equation.

The discriminant is given by b²-4ac.  This is what goes under the square root in the quadratic formula.  Since we will be taking the square root of this, if the discriminant is less than 0, there are no real roots; you cannot have a real square root of a negative number.
If the discriminant is equal to 0, there is 1 real root; the square root of 0 is 0, so the quadratic formula would yield one answer.
If the discriminant is greater than 0, there are 2 real roots.  This is because taking the square root of a positive number gives a positive and negative result.

b in our equation is -7, a is 3 and c is 4:
b²-4ac = (-7)²-4(3)(4) = 49 - 48 = 1

There is 1 real root.

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for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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