Question

9. If ‘α’ and ‘β’ are the zeros of the quadratic polynomial f(x) = x2- 5x + 4, find the value of





1/a+ 1/b



​

Answer 1

Answer:

ANSWER

Since α,β are the zeroes of the polynomial, they are also the roots of the equation x2−5x+k=0

Sum of the roots =α+β=−b/a=5    →(I)

We know from the question that α−β=1   →(II)

(I)+(II)⇒2α=6

⇒α=3

⇒β=2 (by substituting for α in (I))

∴αβ=2×3=6  →(III)

Produuct of the roots =αβ=c/a=k→(IV)

∴k=6 (from (III),(IV))

Hence, the answer is option D.

Answer 2

Answer:

The value is

4

−27

Step-by-step explanation:

Given that α and β are the zeroes of the polynomial

x^2-5x+4x

2

−5x+4

we have to find the value of

\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \beta

α

1

+

β

1

−2αβ

x^2-5x+4x

2

−5x+4

By comparing with standard form ax^2+bx+c=0ax

2

+bx+c=0

⇒ a=1, b=5 and c=4

\text{Sum of zeroes= }\alpha+\beta=\frac{-b}{a}=-\frac{-5}{1}=5Sum of zeroes= α+β=

a

−b

=−

1

−5

=5

\text{Product of zeroes= }\alpha.\beta=\frac{c}{a}=\frac{4}{1}=4Product of zeroes= α.β=

a

c

=

1

4

=4

Now,

\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \beta

α

1

+

β

1

−2αβ

=\frac{\beta+\alpha}{\alpha \beta}-2\alpha \beta=

αβ

β+α

−2αβ

=\frac{5}{4}-2(4)=\frac{5}{4}-8=\frac{-27}{4}=

4

5

−2(4)=

4

5

−8=

4

−27