Question

If alpha and beta are the zeros of the polynomial x^2-5x+6 find value of 1 by alpha square plus one by beta square

Answer 1

hello friend the answer is 13/36

Answer 2

Answer:

13/36

Explanation:

We have given that

$\alpha \: and \: \beta$ are two zeroes of the polyomial x²-5x+6 .

Compare x²-5x+6 with ax²+bx+c,

we get

a = 1 , b = -5 , c = 6

i ) sum of the zeroes = -b/a

$\alpha + \beta = \frac{-(-5)}{1}$

= $5$ ---(1)

ii ) Product of the zeroes = c/a

$\alpha \times \beta = \frac{6}{1}$

= $6$ ---(2)

iii) $\frac{1}{(\alpha)^{2}} + \frac{1}{(\beta)^{2}}$

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

= $5^{2}-2\times 6$

= $25-12$

= $13$

Now ,

$\frac{1}{(\alpha)^{2}} + \frac{1}{(\beta)^{2}}$

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

= $\frac{13}{6^{2}}$

= $\frac{13}{36}$

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