Question

if a and b are zeros of the polynomial x² -x-6 , then find quadratic polynomial whose zeroes are (3a-2b) and (2a+3b)​

Answer 1

$\bf\underline{\red{Answer}}$

Polynomials written in form of x² - Sx + P, represent S as sum of their roots and P as product of roots.

So, here, if a and b are roots:

→a+b = 3

→ ab 2

Thus, (a + b)² = 3² a² + b² + 2ab = 9 → a² + b² = 9 - 2(-2) = 9 + 4 = 13

Let the required polynomial is x² - px + q,

SO

p=(2a + 3b) + (3a + 2b)

p=2a + 3b + 3a + 2b = 5a + 5b

p= 5(a + b) = 5(3) = 15

Whereas,

q= (2a + 3b)(3a + 2b)

q=6(a² + b²) + 13ab

q = 6(13) + 13(-2) = 13(6-2) = 13(4)

q=52

Hence, required polynomial is:

x² - 15x + 52

Hope you Helps:)