Question

f α and β are the zeroes of p(x) = x² – 5x + 3, then find the value of α + β– αβ a) 1 b) 2 c) 3 d) 5​

Answer 1

Answer:

(1/α) + (1/β) - 2αβ = -27/4

Step-by-step explanation:

f (x) = x² - 5x + 4

α + β are the zeros of the polynomial.

Then α + β = -b/a = 5

αβ = c/a = 4

Now (1/α) + (1/β) - 2αβ = [α + β / αβ] - 2αβ = 5/4 - 8 = 5 - 32/4 = -27/4

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If α and β are the zeroes of p(x) = x² – 5x + 3, then find the value of α + β– αβ

a) 1

b) 2

c) 3

d) 5

CONCEPT TO BE IMPLEMENTED

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

EVALUATION

Here the given Quadratic polynomial is

p(x) = x² – 5x + 3

Now it is given that α and β are the zeroes of p(x)

Thus we have

Sum of the zeroes

= α + β

= 5

Product of the zeroes

= αβ

= 3

We get

α + β – αβ

= 5 - 3

= 2

FINAL ANSWER

Hence the correct option is b) 2

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