Question

Hi fRIENDS !!
Find the zeroes of each of the following polynomials and verify the
relationship between the zeros and their coefficients
x2 – 18 – 3x

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Answer 1

Aɴꜱᴡᴇʀ

$\huge \sf zeros = - 3 \: and \: 6$

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Gɪᴠᴇɴ

☛ x² - 18 - 3x = 0

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ᴛᴏ ꜰɪɴᴅ ᴛᴏ ᴘʀᴏᴠᴇ

The zeros

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Sᴛᴇᴘꜱ

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,

Zeros of polynomial = -3 & 6

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

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Verification:-

Relation 1 : —

⋆ Sum of zeros = - b / a

⇒ -3 + 6 = -(-3)/1

⇒ 3 = 3/1

⇒ 3 = 3 [Hence verified!]

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.

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$

Answer 2

❣️☺️$</p><p>{\huge {\overbrace {\underbrace {\purple { Answer }}}}}$☺️❣️

$x^2-3x-18=0\\x^2-6x+3x-18=0\\x(x-6)+3(x-6)=0\\(x-6)(x+3)=0$

$\huge\boxed{\fcolorbox{white}{pink}{x=(-3),6}}$

hope this helps uh☺️