Find the Zeroes of the Polynomial x2 + x/6 -2 and Verify the Relation between the Coefficient and Zeroes of the Polynomial
To find the zeroes of the polynomial x2 + x/6 - 2, we set the polynomial equal to zero and solve for x:
x2 + x/6 - 2 = 0
Multiplying the entire equation by 6 to eliminate the fraction:
6x2 + x - 12 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
(2x + 3)(3x - 4) = 0
Setting each factor equal to zero:
2x + 3 = 0 or 3x - 4 = 0
Solving each equation:
2x = -3 --> x = -3/2
3x = 4 --> x = 4/3
So, the zeroes of the polynomial x2+ x/6 - 2 are x = -3/2 and x = 4/3.
Now, let's verify the relation between the coefficients and zeroes of the polynomial. For a quadratic polynomial in the form ax2 + bx + c, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.
In this case, the coefficient of x2 is 1, the coefficient of x is 1/6, and the constant term is -2.
The sum of the zeroes: (-1/6) / 1 = -1/6
The product of the zeroes: (-2) / 1 = -2
We can observe that the sum of the zeroes (-1/6) matches the negative coefficient of x (-1/6), and the product of the zeroes (-2) matches the constant term (-2). Hence, the relation between the coefficients and zeroes of the polynomial is verified.
The zeros of the polynomial x2+ x/6 - 2 are x = -3/2 and x = 4/3.
- Find the Zeros of the Quadratic Polynomial 4u²+8u and Verify the Relationship between the Zeros and the Coefficient.
- Write the Zeros of the Quadratic Polynomial f(x) = 4√3x² + 5x - 2√3
- If the sum of Zeros of the Quadratic Poynomial p(x) = kx²+2x+3k is Equal to their Product Find the Value of k
- Find the Zeros of the Quadratic Polynomial √3x² - 8x + 4√3
- If α and β are the Zeros of the Quadratic Polynomial f(x) = ax2 + bx + c, then Evaluate
Commentswrite a comment