Question

If alpha and beta are the zeros of the quadratic polynomial x square - 5 x + 4 find the value of 1 alpha + 1 beta minus 2 alpha beta

Answer 1

Answer:

x²-5x+4

= x²-1x-4x+4

= x(x-1) -4(x-1)

= (x-1)(x-4)

x = 1 or x = 4

alpha = 1 and beta = 4

now,

1 alpha + 1 beta - 2 alpha beta

= 1 + 4 - 2×1×4

= 1+4-8

= -3

ans.

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Answer 2

Correct Question :-

If alpha and beta are the zeroes of the quadratic polynomial x² - 5x + 4. Find the value of 1/ɑ + 1/β - 2ɑβ

Given :-

• P(x) = x² - 5x + 4
• ɑ and β are the zeroes of the polynomial.

To Find :-

• The value of 1/ɑ + 1/β - 2ɑβ.

Solution :-

If ɑ and β are the zeroes of the given quadratic polynomial P(x). Then,

• $\rm{\alpha+\beta=\dfrac{-b}{a}}$

• $\rm{\alpha\times{}\beta=\dfrac{c}{a}}$

Therefore,

$\implies\rm{\alpha+\beta=\dfrac{-(-5)}{1}=5}$

$\implies\rm{{\alpha}{\beta}=\dfrac{4}{1}=4}$

$\hrulefill$

${\therefore}\:\rm{\dfrac{1}{\alpha}+\dfrac{1}{\beta}-2{\alpha}{\beta}=\dfrac{\alpha+\beta}{{\alpha}{\beta}}-2{\alpha}{\beta}}$

Putting the values for (ɑ + β) and (ɑ × β), we get,

$\implies\rm{\dfrac{5}{4}-2(4)}$

$\implies\rm{\dfrac{5}{4}-8}$

$\implies\rm{\dfrac{5-32}{4}=}\:\bold{\dfrac{-27}{4}.}$