Question

(iii) p(x) = x2 - 4 find the zeros of the quadratic polynomial and find the sum of product of the zeros verify relationship to the coefficients

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Answer 1

Step-by-step explanation:

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Answer 2

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) p(x) = x² - 4

Find the zeroes of the Quadratic Polynomial and find the sum and product of the zeroes and verify relationship to the coefficients .

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★ Given :

$\sf \: polynomial = {x}^{2} - 4$

★ To Find :

• The zeroes of the Polynomial .
• Sum and product of zeroes .
• Verify relationship of zeroes to coefficients .

★ Solution :

➜ Finding zeroes -

$\mapsto \rm \: {x}^{2} - 4 = 0$

$\mapsto \rm \: {x}^{2} - {2}^{2} = 0$

$\mapsto \rm \: (x + 2)(x - 2) = 0$

So , either

$\rm \: x + 2 = 0 \\ \leadsto\boxed{ \rm \: x = - 2}$

or

$\rm \: x - 2 = 0 \\ \leadsto \boxed{ \rm \: x = 2}$

So ,

# Zeroes of the Polynomial :

• First zero = -2
• Second zero = 2

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# Sum of zeroes = -2 + 2 = 0

# Product of zeroes = -2×2 = -4

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➜ Verifying Relationship of coefficients and zeroes -

First make the Polynomial in standard form

$\boxed{ \sf \: standard \: form : a {x}^{2} + bx + c}$

$\longrightarrow \rm \: 1 {x}^{2} + 0x + ( - 4)$

So , in this equation ,

• a = 1
• b = 0
• c = -4

$\mapsto \rm \: sum \: of \: zeroes = \frac{ - b}{a}$

$\mapsto \rm \: - 2 + 2 = \frac{ - 0}{1}$

$\mapsto \rm \: 0 = 0$

LHS = RHS Hence Verified !

$\mapsto \rm \: product \: of \: zeroes = \frac{c}{a}$

$\mapsto \rm \: - 2 \times 2 = \frac{ - 4}{1}$

$\mapsto \rm \: - 4 = - 4$

LHS = RHS Hence Verified !

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