find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient. 6x square +x-12
Answers
Given : 6x² + x - 12
To Find : zeros
verify the relationship between the zeros and the coefficient.
Solution:
ax² + bx + c
sum of zeros = - b/a
product of zeroes = c/a
6x² + x - 12
=> a = 6 b = 1 , c = - 12
sum of zeros = - 1/6
product of zeroes = -12/6 = - 2
6x² + x - 12
= 6x² + 9x - 8x - 12
= 3x(2x + 2) - 4(2x + 3)
= (3x - 4)(2x + 3)
To find Zeroes
Equate each with zero
3x - 4 = 0 => x = 4/3
2x + 3 = 0 => x = - 3/2
Zeroes are 4/3 and - 3/2
Sum of Zeroes = 4/3 - 3/2 = (8 - 9)/6 = -1/6
Product of Zeroes = (4/3)(-3/2) = - 2
Sum of zeroes and product of zeroes are same in both cases
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