Question

pls solve dis fast,............​

Answer 1

Answer :

x² + 4x + 4

Step-by-step explanation:

f(x) = x² - 1

f(x) = x² - 1² = (x - 1)(x + 1)

so zeroes will be 1 or (- 1)

I am assuming alpha == a

And assuming beta === b

for that quadratic polynomial a == 1 and b == (- 1)

To find a quadratic polynomial with zeros 2a / b and 2b / a

2a / b = 2 * 1 / (- 1) = - 2

2b / a = 2 * (- 1) / 1 = - 2

Now polynomial :::

x² - (sum of Zeros) x + (product of Zeros)

= x² - [ (- 2) + (- 2) ] x + (- 2)(- 2)

= x² - (- 4) x + 4

= x² + 4x + 4

So your polynomial is x² + 4x + 4

Answer 2

${\red{\underline{\underline{\red{Given:-}}}}}$

• α & β are the zeroes of the quadratic polynomial f(x) = x² - 1

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The quadratic polynomial whose zeroes are $\bf \dfrac{2\alpha}{\beta}$ and $\bf \dfrac{2\beta}{\alpha}$

${\green{\underline{\underline{\bold{Solution:-}}}}}$

α & β are the zeroes of the quadratic polynomial

= x² - 1

= x² - 1²

According to the expansion:- a² - b² = (a+b) (a-b)

➪ x² - 1² = (x+1) (x-1)

➪ x = 1 , -1

Therefore

α = 1 and β = -1

Now we have to find the quadratic equation who zeroes are $\bf \dfrac{2\alpha}{\beta}$ and $\bf \dfrac{2\beta}{\alpha}$

If the zeroes are given the quadratic equation is given by

x² - (sum of zeroes) x + product of zeroes = 0

Sum of zeroes:-

Sum of zeroes = $\bf \dfrac{2\beta}{\alpha} + \dfrac{2\alpha}{\beta}$

$\implies \bf \frac{2 { \beta}^{2} + 2 { \alpha}^{2} }{ \alpha \beta} ........(1)$

Substituting α = 1 and β = -1 in equation (1)

$\bf \frac{2 { (- 1)}^{2} + 2 { (1)}^{2} }{ (1) ( - 1)}$

$\implies \bf \frac{(2 \times 1) +(2 \times 1) }{ - 1}$

$\implies \bf \frac{2 + 2}{ - 1}$

$\implies \bf \frac{4}{ - 1} = - 4$

Product of zeroes:-

$\bf \: \frac{2 \alpha}{ \beta} \times \frac{2 \beta}{ \alpha}$

$\implies \bf \frac{4 \alpha \beta}{ \alpha \beta} = 4$

x² - (sum of zeroes) x + product of zeroes = 0

$\implies \bf {x}^{2} - ( - 4)x + 4 = 0$

$\implies \bf {x}^{2} + 4x + 4 = 0$

Therefore the required quadratic polynomial is

$\implies \bf {x}^{2} + 4x + 4$