The zeroes of the polynomial 3x2+11x−4 are :
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Step-by-Step Solution
Step 1: Identify coefficients
The given polynomial is a quadratic equation of the form ax2+bx+c=0. We need to identify the coefficients a, b, and c from the given polynomial 3x2+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 112=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.