Question

find the videos of the following were deleted polynomial and verify the relationship 1) x 2 -5​

Answer 1

Step-by-step explanation:

Correct Question :-

• Find the zeroes of the polynomial p(x) = x² - 5 and verify the relationship

Solution :-

Given :-

• p(x) = x² - 5

To Find -

• Zeroes of the polynomial
• Verify the relationship between the zeroes and the coefficient

Now,

→ x² - 5

By using the identity of a² - b² = (a + b)(a - b), we get :

→ (x)² - (√5)²

→ (x + √5)(x - √5)

Zeroes are -

→ x + √5 = 0 and x - √5 = 0

→ x = -√5 and x = √5

Verification :-

As we know that :-

• α + β = -b/a

→ -√5 + √5 = -(0)/1

→ 0 = 0

LHS = RHS

And

• αβ = c/a

→ -√5 × √5 = -5/1

→ -5 = -5

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

$\large{\underline{\bf{\purple{Given:-}}}}$

• ✦ p(x) = x² - 5

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• ✦ we need to find the zeroes of polynomial and also find the relationship between the zeroes and coefficients.

$\huge{\underline{\bf{\red{Solution:-}}}}$

➜ p (x) = x² - 5

$\:\boxed { \pink{ \bf {a}^{2} - {b}^{2} = (a + b)(a - b) }}$

$\leadsto \rm\:\: {x}^{2} - (\sqrt{5}) ^{2} \\ \\\leadsto \rm\:\: =(x + \sqrt{5})(x - \sqrt{5} ) \\ \\\leadsto \rm\:\:x + \sqrt{5} = 0 \\ \\ \leadsto \bf\:\:x = - \sqrt{5} \\\\ \:\:\:\:\:\bf{or}\\\\ \leadsto \rm\:\: x - \sqrt{5} = 0 \\ \\ \leadsto \bf\:\:x = \sqrt{5}$

• Let α = - √5 and β = √5

Now,

Relationship between zeroes and coefficients:-

sum of zeroes = - b/a

• (α + β) = - b/a

$\leadsto \rm\:\:$(- √5 +√5) = 0/1

$\leadsto \:0=0 \:\:$

Product of zeroes = c/a

• αβ = c/a

$\leadsto \rm\:\:$ -√5 × √5 = -5/1

$\leadsto \bf\:\:-5 = -5$

LHS = RHS

Hence relationship is verified

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