Question

Let a and B are the zeroes of a quadratic polynomial 2x2 - 5x - 6 then form a
quadratic polynomial whose zeroes are a + B and aß. (CBSE 2011)​

Answer 1

Note : Here I am using m and n

instead of Alfa and beta.

Given:

m and n are zeroes of a quadratic polynomial 2x²-5x-6

To find:

Form of a quadratic polynomial

whose zeroes are (m+n) and

mn

Explanation:

Compare given Quadratic polynomial 2x²-5x-6 with

ax²+bx+c , we get

a = 2 , b = -5 , c =-6

i )sum of the zeroes = -b/a

= -(-5)/2 = 5/2

m+n = 5/2 -----(1)

ii ) product of the zeroes = c/a

=>mn = (-6)/2 = -3 ---(2)

Now ,

(m+n) and mn are two zeroes,

iii ) Sum of the zeroes

= (m+n) + mn

= 5/2 + (-3)

= ( 5 - 6)/2

= -1/2 ----(3)

iv ) product of the zeroes

= (m+n)×mn

= (5/2) ×(-3)

= -15/2 ----(4)

_______________________

Form of a quadratic polynomial

is

k[x²-(sum of the zeroes)x+product of the zeroes]

______________________

Here,

k[ x²-(-1/2)x+(-15/2)]

For all real values of k it is true.

if k = 2,

2[x²+(1/2)x-15/2]

= 2x²+x-15

Therefore,

Required form of a polynomial

is 2x²+x-15