Question

if alpha and beta are zeros of x2 -5x + 4 find alpha squared beta +alpha bera squared

Answer 1

Hey!!!!!

_________

We have

=> x² - 5x + 4

Thus

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = 5$
and

$\alpha \beta = \frac{c}{a}$

$\alpha \beta = 4$

To Find :
${ \alpha }^{2}{\beta} + { \beta }^{2}{\alpha}$

= alpha beta(alpha + beta)

Replacing Value

=> 4(5)

=> 20

____________

Method 2 :-

We have, x² - 5x + 4 = 0

=> x² - 4x - x + 4 = 0

=> x(x - 4) - (x - 4) = 0

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

Thus

$\alpha = 4 \: and \: \beta = 1$

${ \alpha }^{2}{\beta} + { \beta }^{2}{\alpha}$
Thus
=> alpha beta(alpha + beta)

=> 4(4 + 1)

=> 4(5)

=> 20
_____________

Hope this helps ✌️

Answer 2

sum of roots = (-b/a) = -(-5/1) = 5
product of roots= (c/a) = (4/1) = 4

alpha + beta = 5
(alpha)x(beta) = 4

by solving we get
alpha= 4
beta=1