Question

find the zero of the polynomial p(x)=6x^2-7x-3 and verify the relationship between the zeroes and its coefficients​

Answer 1

Answer:

Given equation,

→ 6x² - 7x - 3 = 0

We have to find out the roots of this equation and also verify the relationship between roots and coefficients.

So,

→ 6x² - 7x - 3 = 0

→ 6x² - 9x + 2x - 3 = 0

→ 3x(2x - 3) + 1(2x - 3) = 0

→ (3x + 1)(2x - 3) = 0

→ (3x + 1) = 0 or (2x - 3) = 0

→ x = -1/3, 3/2

So, the values of x are- -1/3, 3/2.

Verification:

We know that, if ax² + bx + c = 0, then,

→ Sum of roots = -b/a

→ Product of roots = c/a

So,

-1/3 + 3/2

= (-2+9)/6

= 7/6

Also,

-b/a

= -(-7)/6

= 7/6

So,

→ Sum of roots = -b/a (Verified)

Again,

-1/3 × 3/2

= -1/2

Also,

c/a

= -3/6

= -1/2

So,

→ Product of roots = c/a (Verified)