Question

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Answer 1

Explanation:

4s

2

−4s+1

Factorize the equation, we get(2s−1)(2s−1)

So, the value of 4s

2

−4s+1 is zero when 2s−1=0,2s−1=0, i.e., when s=

2

1

or s=

2

1

.

Therefore, the zeros of 4s

2

−4s+1 are

2

1

and

2

1

.

Now,

⇒Sum of zeroes =

2

1

+

2

1

=1=−

4

−4

=−

Coefficient of s

2

Coefficient of s

⇒Product of zeros =

2

1

×

2

1

=

4

1

=

4

1

=

Coefficient of s

2

Constant term

Answer 2

Question -

Find the zeroes of following quadratic polynomials and verify the relationship between the zeroes and the co-ffecients

• 4x² - x - 5

Solution -

${4x}^{2} - x - 5 = 0$

$= > {4x}^{2} - (5 + 4)x - 5 = 0$

$= > {4x}^{2} - 5x + 4x - 5 = 0$

$= > x(4x - 5) + 1(4x - 5)$

$= > (x + 1)(4x - 5)$

Now we will find zeroes,

$x + 1 = 0$

$= > x = ( - 1)$

$4x - 5 = 0$

$= > 4x = 5$

$= > x = \frac{5}{4}$

$\alpha = ( -1 ) \: and \: \beta = \frac{5}{4}$

Relationship between the zeroes,

a = 4

b = (-1)

c = (-5)

$Sum \: of \: zeroes = \frac{ - b}{a}$

$= > \alpha + \beta = \frac{( - b)}{a}$

$= > ( - 1) + \frac{5}{4} = \frac{ - ( - 1)}{4}$

$= > \frac{1}{4} = \frac{1}{4}$

$Product \: of \: zeroes = \frac{c}{a}$

$\alpha \beta = \frac{c}{a}$

$= > ( - 1) \times (\frac{5}{4}) = \frac{( - 5)}{4}$

$= > \frac{ - 5}{4} = \frac{ - 5}{4}$

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