Question

if α and β are the zeroes of the polynomial 4x2+4x+1, then form a qiadrayic polynamial whose zeroes are 2α and 2β​

Answer 1

the required equation is -- x^2-x+1

Answer 2

Answer:

4x² + 4x + 1

⇒ 4x² + 2x + 2x + 1

⇒ 2x ( 2x + 1 ) +1 ( 2x + 1 )

⇒ ( 2x + 1 ) ( 2x + 1 )

By zero product rule,

α = - 1/2 and β = - 1/2

We need to find, a quadratic polynomial whose zeroes are 2α and 2β.

2α = 2 * (-1/2) = - 1

2β = 2 * (-1/2) = - 1

New quadratic polynomial -

$\bf x {}^{2} +( \alpha + \beta )x - ( \alpha \beta ) \\ \\ \sf x {}^{2} + ( - 1 - 1)x - \{- 1 \times ( - 1) \} \\ \\ \sf x {}^{2} - 2x - 1$

Hence, required polynomial is x² - 2x - 1.