Question

find the zeros of the quadratic polynomial 6x square - 3 - 7 x and verify the relationship between the zeros and the coefficient of the polynomial​

Answer 1

Given polynomial is 6x² - 3 - 7x or 6x² - 7x - 3.

We have to find the zeros of the above polynomial and verify the relationship between the zeros and coefficient.

To find the zeros the given polynomial we have to solve it by splitting the middle term.

Since it is in the form ax² + bx + c = 0.

So,

→ 6x² - 7x - 3 = 0

→ 6x² - 9x + 2x - 3 = 0

→ 3x(2x - 3) +1(2x - 3) = 0

→ (2x - 3)(3x + 1) = 0

On comparing we get,

→ x = 3/2, -1/3

Therefore, the zeros of the polynomial are 3/2 and -1/3.

Verification

We know that,

Sum of zeros = -b/a and Product of zeros = c/a

And in a given polynomial;

a = 6, b = -7 and c = -3

Now, Sum of zeros = -b/a

3/2 + (-1/3) = -(-7)/6

(9 - 2)/6 = 7/6

7/6 = 7/6

Product of zeros = c/a

(3/2) × (-1/3) = -3/6

-1/2 = -1/2

Answer 2

$6 {x}^{2} - 7x - 3 \\ = 6 {x}^{2} + 2x - 9x - 3 \\ 2x(3x + 1) - 3(3x - 1) = 0 \\ (2x - 3)(3x - 1) = 0 \\ 2x - 3 = 0 \: \: \: \: \: \: \: \: \: \: \: 3x - 1 = 0 \\ 2x = - 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3x = 1$

x = 3/2 x = 1/3

The zeroes of x are -3/2 and 1/3