Question

6x^2-7x-3
Relation between zero & Co-efficients​

Answer 1

Solution:

Given equation,

→ 6x² - 7x - 3 = 0

By splitting the middle term, we get,

→ 6x² - 9x + 2x - 3 = 0

→ 3x(2x - 3) + 1(2x - 3) = 0

→ (3x + 1)(2x - 3) = 0

By Zero-product rule,

→ 3x + 1 = 0 or 2x - 3 = 0

→ x = -1/3, 3/2

So, the roots of the given equation are -1/3 and 3/2

Verification:

Comparing the given equation with ax² + bx + c = 0, we get,

→ a = 6

→ b = -7

→ c = -3

→ Sum of roots = -b/a = 7/6

Now,

-1/3 + 3/2

= (-2 + 9)/6

= 7/6

So,

→ Sum of roots = -b/a – Verified.

Again,

→ Product of roots = c/a = -3/6 = -1/2

Now,

-1/3 × 3/2

= -1/2

So,

→ Product of roots = c/a – Verified.

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