Question

if alpha and beta are the zeroes of the quadratic polynomial p(x)=x2+5x-6,find the polynomial whose zeroes are 2aplha + 1 and 2beta + 1​

Answer 1

Solution :

The given polynomial is

f (x) = x² - 5x + 6

⇒ f (x) = x² - 3x - 2x + 6

⇒ f (x) = x (x - 3) - 2 (x - 3)

⇒ f (x) = (x - 3) (x - 2)

Let, α = 3 and β = 2 [ ATQ ]

To find : the polynomial whose zeroes are (2α + 1) and (2β + 1).

Now, 2α + 1 = (2 * 3) + 1 = 7

and 2β + 1 = (2 * 2) + 1 = 5

∴ the required polynomial is

g (x) = {x - (2α + 1)} {x - (2β + 1)}

⇒ g (x) = (x - 7) (x - 5)

⇒ g (x) = x² - 7x - 5x + 35

⇒ g (x) = x² - 12x + 35