Question

If alpha and beta are the zeroes of x2 - 5x + 4 ,then find all quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha

Answer 1

Answer:

Hope this helps you

Step-by-step explanation:

x2-5x+4=x2-(1+4)x+4

=x2-x-4x+4

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

=(x-1)(x-4)

Therefore the zeros of the given polynomial are 1 & 4

alpha +1/beta = 1+1/4 =5/4

beta + 1/alpha = 4+1/1 = 4 + 1 = 5

Answer 2

$\alpha+\frac{1}{\beta}=\frac{5}{4}$

$\beta+\frac{1}{\alpha}=5$

Step-by-step explanation:

Given : If alpha and beta are the zeroes of $x^2 - 5x + 4$.

To find : All quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha

Solution :

Quadratic equation $x^2 - 5x + 4=0$,

Applying middle term split,

$x^2 - x-4x + 4=0$

$x(x-1)-4(x-1)=0$

$(x-1)(x-4)=0$

$x=1,4$

So, the roots of the polynomial are $\alpha =1$ and $\beta =4$

Substitute the value in the expression,

$\alpha+\frac{1}{\beta}=1+\frac{1}{4}$

$\alpha+\frac{1}{\beta}=\frac{5}{4}$

and $\beta+\frac{1}{\alpha}=4+\frac{1}{1}$

$\beta+\frac{1}{\alpha}=5$

#Learn more

If alpha and beta are the zeroes of x2 - 5x + 4 ,then find the value of 1/alpha + 1/beta-2alphabeta

https://brainly.in/question/4490671