Question

Find the zeroes of 12 x 2 – 7x + 1 , and verify the relationship between the zeroes and the coefficients.

Answer 1

Given :-

12x² - 7x + 1

To Find :-

Zeroes

Solution :-

12x² - 7x + 1

Spilt the middle term

12x² - (4x + 3x) + 1

12x² - 4x - 3x + 1

4x(3x - 1) - 1(3x - 1)

(4x - 1)(3x - 1)

Value of x

4x - 1 = 0

x = 1/4

3x - 1 = 0

x = 1/3

Now

On comparing the given equation with ax² + bx + c. We get,

a = 12

b = -7

c = 1

Sum of zeroes = -b/a

1/4 + 1/3 = -(-7)/12

3 + 4/12 = 7/12

7/12 = 7/12

Product of zeroes = c/a

1/4 × 1/3 = 1/12

1/12 = 1/12