Question

If α & β are zeroes of $2x^{2} - 5x + 7$, find the polynomial whose zeroes are 2α + 3β and 3α + 2β.

Answer 1

QUESTION :-

If α & β are zeroes of 2x²- 5x + 7, find the polynomial whose zeroes are 2α + 3β and 3α + 2β.

SOLUTION :-

➠ p(x) = 2x²-5x+7 -----(given)

➠ let, the two zeroes be α & β.

➠ .°. sum of zeroes = α + β

➠ (-b)/ a = -(-5)/2 = 5/2-------(1)

➠ .°. product of zeroes = αβ

➠ c /a = 7/2 ------------(2)

➠ zeroes of polynomial are (2α+3β) and (3α+2β) .

➠ since, α + β = (2α + 3β) + (3α + 2β)

➠ 5α + 5β = 5(α+β)

➠ from (1) , we get

➠ 5(α+β) = 5×5/2 = 25/2.

➠ .°. α + β = 25/2.

➠ αβ = (2α +3β)(3α +2β)

➠ αβ = 6α² +4αβ + 9αβ + 6β²

➠ αβ = 6(α²+β²) +13αβ

➠ αβ = 6[(α+β)² -2αβ] -13αβ

➠ αβ = 6[(5/2)² - 2(7/2)] + 13 * 7/2 ----[from (1) & (2)]

➠ αβ = 6[25/4 -7] +91/2

➠ αβ = 6*(-3)/4 + 91/2 = -9/2 + 91/2 = 82/2 = 41

➠ .°. αβ = 41.

therefore, the polynomial obtained is.

➠ g(x)= x²-(α+β)x + αβ

➠ .°. g(x) = x² - (25/2)x + 41.

Answer 2

$\rule{300}{2}$

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R:-}}}}$

See this attachment

This is the best possible answer

$\large{\boxed{\mathbf\pink{\fcolorbox{cyan}{black}{Hope\:you\:have}}}}$

$\large{\boxed{\mathbf\pink{\fcolorbox{red}{yellow}{Understood}}}}$

$<marquee>♥️Please mark it as♥️</marquee>$

$\huge\underline\mathcal\red{Brainliest}$

$</p><p>\huge{\boxed{\mathbb\green{\fcolorbox{red}{blue}{Thank\:You}}}}$

$\rule{300}{2}$