Question

Find the zero polynomial and verify the relationship between zero and Coefficient 2 x square minus x minus 1​

Answer 1

Answer:-

Zeros of polynomial = -1/2 & 1

Given polynomial:-

☛ 2x² - x - 1 = 0

We can find zeros by factorization method:-

→ 2x² - x - 1 = 0

→ 2x² - 2x + x - 1 = 0

→ 2x(x - 1) + 1(x - 1) = 0

→ (2x + 1)(x - 1) = 0

→ 2x = -1 or x = 1

→ x = -1/2 or x = 1

Hence,

Zeroes of polynomial =

$\frac{ - 1}{2} and1$

Verification:-

Here, zeros are -1/2 & 1

Comparing the given polynomial with ax² + bx + c we get:-

Coefficient of x²(a) = 2

Coefficient of x(b) = -1

Constant term(c) = -1

Relationship 1:-

☛ Sum of zeros = -b/a

→ (-1/2 + 1) = -(-1)/2

→ (-1 + 2)/2 = 1/2

→ 1/2 = 1/2 [Hence verified!]

Relationship 2:-

☛ Product of zeros = c/a

→ (-1/2 × 1) = -1/2

→ -1/2 = -1/2 [Hence verified!]