Question

a,b are zeroes of quadratic
polynominal x²-3x+2. Then
value
of a +B +aB

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Answer 1

Correct Question :

A and B are the zeroes of the polynomial x² - 3x + 2. Then, find the vale of A + B + AB.

Given :  f(x) = x² - 3x + 2

• By Middle Term Factorisation -

⇒ x² - 2x - x + 2

⇒ x(x - 2) - 1(x - 2)

⇒ (x - 1)(x - 2)

To find zeroes these factors should be equal to 0.

• Using Zero Product Rule -

⇒ x - 1 = 0 and x - 2 = 0

⇒ x = 1 and x = 2

A.T.Q., A and B are the zeroes. So, A = 1, B = 2

A + B + AB = 1 + 2 + (1)(2)

⇒ 1 + 2 + 2 = 5

                         OR

Given : x² - 3x + 2

On comparing this with ax² + bc + c, we get

            a = 1, b = - 3, c = 2

Now,

• Sum of zeroes = A + B = - b/a

                         = - (- 3)/1 = 3

• Product of zeroes = AB = c/a

                              = 2/1 = 2

Value of A + B + AB -

⇒ 3 + 2 = 5