Question

if alpha and beta are the zeros of the polynomial f x is equal to x squared minus 6 X + K find the value of k such that a Alpha square + beta square is equal to 40

Answer 1

See solution above in the image
If alpha and beta are the zeros of f(x) then it's satisfies the equation
Also alpha + beta = 6
Then solve equation and putting given values

Answer 2

Answer:

Value of k = -2

Explanation:

Given quadratic expression :

f(x)=x²-6x+k

and

$\alpha\: and\: \beta \:are \:two \:zeroes \:of \:f(x)$

Now ,

Compare f(x)=x²-6x+k with

ax²+bx+c , we get

a = 1 , b = -6 , c = k

i) sum of the zeroes = -b/a

$\implies \alpha + \beta$

=$\frac{-(-6)}{1}$

= $6$ ----(1)

ii) Product of the zeros =c/a

$\alpha\beta = \frac{k}{1}$

$\implies \alpha\beta = k$ -----(2)

It is given that ,

$\alpha^{2}+\beta^{2}=40$

$\implies (\alpha^+\beta)^{2}-2\alpha\beta=40$

/* By algebraic identity :

a²+b² = (a+b)²-2ab */

$\implies 6^{2}-2k=40$

/* from (1) and (2) */

$\implies 36-2k=40$

$\impliea -2k = 40-36$

$\implies -2k = 4$

$\implies k = \frac{4}{-2}$

$\implies k = -2$

Therefore,.

Value of k = -2

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