Question

If a and b are the zeroes of the quadratic polynomial f(x) = x 2 - 3x - 2, then find the polynomial whose zeroes are : (2a + 3b) and (3a + 2b)

Answer 1

Answer:

x² - 15x + 52

Step-by-step explanation:

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 = 6a² + 4ab + 9ab + 6b²

q =6(a² + b²) + 13ab

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

q = 52

Hence, required polynomial is:

x² - 15x + 52