Question

Answer the following (SA)
11. Find the zeroes of 4x2 - 4x +1 and verify the relationship of zeroes.
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Answer 1

Step-by-step explanation:

Given -

• p(x) = 4x² - 4x + 1

To Find -

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

Now,

→ 4x² - 4x + 1

By middle term splitt :-

→ 4x² - 2x - 2x + 1

→ 2x(2x - 1) - 1(2x - 1)

→ (2x - 1)(2x - 1)

Zeroes are -

→ 2x - 1 = 0 and 2x - 1 = 0

→ x = 1/2

Verification :-

As we know that :-

• α + β = -b/a

→ 1/2 + 1/2 = -(-4)/4

→ 1 = 1

LHS = RHS

And

• αβ = c/a

→ 1/2 × 1/2 = 1/4

→ 1/4 = 1/4

LHS = RHS

Hence,

Verified..

It snows that our answer is absolutely correct.

Answer 2

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

✰ p(x) = 4x² - 4x +1

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

✰ we need to find the zeroes of the given polynomial and also find the relationship between the zeroes and coefficients.

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

$: \implies \sf\:4x^2-4x+1$

$: \implies \sf4x^2-2x-2x+1$

$: \implies \sf2x(2x-1)-1(2x-1)$

$: \implies \sf\:(2x-1)(2x-1)$

$: \implies \sf\:{\pink{x=\frac{1}{2}\:or\:x=\frac{1}{2}}}$

Now,

Relationship between the zeroes and coefficients:-

$: \implies \sf\alpha+\beta=\frac{-b}{a}$

$: \implies \sf\alpha\beta=\frac{c}{a}$

Let α = 1/2

and β =1/2

sum of zeroes:-

$: \implies \sf$1/2+1/2= -(-4)/4

$: \implies \sf$1 = 1

Product of zeroes:-

$: \implies \sf$1/2 × 1/2 = 1/4

$: \implies \sf$ 1/4 = 1/4

So,

LHS = RHS

Hence Relationship is varified.

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