The zeroes of the polynomial $3x^2 + 11x - 4$ are :

Step 1: Identify coefficients

The given polynomial is a quadratic equation of the form $ax^2 + bx + c = 0$. We need to identify the coefficients $a$, $b$, and $c$ from the given polynomial $3x^2 + 11x - 4$.

Step 2: Apply the quadratic formula

To find the zeroes of a quadratic polynomial, we can use the quadratic formula. Substitute the values of $a=3$, $b=11$, and $c=-4$ into the formula.

Step 3: Substitute values and simplify

Substitute the identified values into the quadratic formula and perform the calculations. First, calculate the term under the square root, which is the discriminant.

Step 4: Calculate the discriminant

Calculate $11^2 = 121$ and $4(3)(-4) = -48$. Then, $121 - (-48) = 121 + 48 = 169$. The square root of 169 is 13.

Step 5: Find the two zeroes

Now, we separate the equation into two cases: one with the plus sign and one with the minus sign, to find the two distinct zeroes of the polynomial.

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