Question

if a and b are the zeroes of the polynomial x2-5x+6 then what is the value of a-b

Answer 1

Polynomial p(x) = x2 -5x + k.

a – b = 1  ………..(i)  (Given)

Sum of the zeroes,

a + b = 5  ……………..(ii)

Solving (i) and (ii), we get

a= 3 and b = 2.

Now product of the zeroes is given by,

ab= (constant term)/ (coefficient of x2)

ab= k

k = 3 × 2

k = 6.

Answer 2

x=a and x=b
so
put the value of x=a in quadratic polynomial
a²-5a+6
spitting middle term
a²-3a-2a+6
a(a-3)-2(a-3)
(a-2)(a-3)
so a=2 or 3
now value of x=b
b²-5b+6
spitting middle term
b²-3b-2b+6
b(b-3)-2(b-3)
(b-2)(b-3)
so b=2 or 3
so value of a-b
that is 2-2 or 3-3= 0
finally value of a-b=0
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