Question

3) Find the zeroes of each of the following polynomials and verify the
relationship between the zeros and their coefficients
x2 – 18 – 3x
pls fast​

Answer 1

AnswEr:-

Zeros of polynomial = -3 & 6

$\rule{200}{2}$

Explanation:-

Given polynomial :-

☛ x² - 18 - 3x = 0

We can easily find zeros of the polynomial by factorization method:-

⇒ x² - 18 - 3x = 0

⇒ x² - 3x - 18 = 0

⇒ x² - 6x + 3x - 18 = 0

⇒ x(x - 6) + 3(x - 6) = 0

⇒ (x + 3)(x — 6) = 0

⇒ x = -3 or x = 6

Therefore,

$\therefore\underline{\textsf{Zeros of polynomial ={\textbf{ -3 \& 6 }}}}$

$\rule{200}{1}$

Here,by comparing with standard form of quadratic polynomial ax² + bx + c we get:-

• Coefficient of x²(a) = 1
• Coefficient of x(b) = -3
• Constant term (c) = -18

Verification:-

Relation 1 : —

⋆ Sum of zeros = - b / a

⇒ -3 + 6 = -(-3)/1

⇒ 3 = 3/1

⇒ 3 = 3 [Hence verified!]

$\rule{150}{1}$

Relation 2:-

⋆ Product of zeros = c / a

⇒ -3 × 6 = -18/1

⇒ -18 = -18 [Hence verified!]

Therefore,

Relation b/w zeros and coefficients of polynomial is verified.

Answer 2

firstly find sum and product then make zeros and then find relationship