Question

the sum of the squares of the zeroes of the polynomial x^2-5x+8

a) 25
b) 16
c) 9
d) 18 ​

Answer 1

For polynomial ax²+bx+c, Sum of roots =(-b)/a, so for x²-5x+8; sum of roots =5; Product of roots =c/a=8; alpha+beta= 5, Now square on both sides alpha ²+beta²+2×alpha ×beta = alpha ²+beta²+2×8=25; alpha ²+beta²=25-16=9; Hence the sum of squares of roots are 9(c); Please mark the answer as brainliest.

Answer 2

Let the zeros (roots) of the polynomial

${x}^{2} - 5x + 8$

be

$\alpha \: and \: \beta$

Then, from the polynomial, we can say that...

$\alpha + \beta = 5 \\ \alpha \times \beta = 8$

Now,

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

$= {5}^{2} - 2 \times 8$

$= 25 - 16$

$= 9$

C is correct

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