Question

If \(α\) and \(β\) are the zeroes of the polynomial \(f(x)=6x^2+x-2\), then the sum of zeroes is

• A. \(\frac 16\)
• B. \(-\frac 16\)
• C. \(-\frac 13\)
• D. \(\frac 13\)

Answer 1

The Correct Option is B

Given the quadratic polynomial f(x) = 6x² + x - 2 with zeroes α and β.

For any quadratic polynomial of the form f(x) = ax² + bx + c:

• Sum of zeroes (α + β) = -b/a
• Product of zeroes (αβ) = c/a

Applying this to our polynomial:

• a = 6 (coefficient of x²)
• b = 1 (coefficient of x)
• c = -2 (constant term)

Calculating the sum of zeroes:

α + β = -b/a = -1/6

Therefore, the sum of the zeroes is -1/6.

The correct answer is: (2) -1/6