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Question Number 33322 by Rio Mike last updated on 15/Apr/18

a) {p x}^{2} + 3 x + q = 0 h a s r o o t s

[\frac{α + β}{α β}] \times α β

f i n d p a n d q i f

x^{2} - 7 x + 4 = 0 w i t h r e a l a n d

d i s t i n c t r o o t s h a s s a m e r o o t s . .

b) i f α a n d β a r e r o o t s o f

x^{2} + k x + 2 k + 8 = 0 .

a) f i n d k i f o n e r o o t i s t w i c e t h e o t h e r .

Commented by Rio Mike last updated on 15/Apr/18

y e s s i r t a k e i t t h e s e w a y i t r i e d s o l v i n g i t

x^{2} + k x + 2 k + 8 = 0

α + β = - k a n d α β = 2 k + 8

l e t o n e r o o t b e α a n d t h e o t h e r 2 α

{S O R}_{n} = α + 2 α = - k \Rightarrow \frac{3 α}{3} = \frac{- k}{3}

α = \frac{- k}{3}

{P O R}_{n} α (2 α) = 2 k + 8

2 α^{2} - 2 k - 8 = 0

2 {(\frac{- k}{3})}^{2} - 2 k - 8 = 0

k^{2} - 9 k - 36 = 0

k = 3 o r k = 12

Commented by MJS last updated on 15/Apr/18

x^{2} - 7 x + 4 = 0

x = \frac{7}{2} \pm \sqrt{\frac{49}{4} - 4} = \frac{7}{2} \pm \frac{\sqrt{33}}{2}

α = \frac{7 - \sqrt{33}}{2}

β = \frac{7 + \sqrt{33}}{2}

{p x}^{2} + 3 x + q = 0

x^{2} + \frac{3}{p} x + \frac{q}{p} = 0

\frac{3}{p} = - 7 \Rightarrow p = - \frac{3}{7}

\frac{q}{p} = 4 \Rightarrow q = - \frac{12}{7}

- \frac{3}{7} x^{2} + 3 x - \frac{12}{7} = 0

Commented by MJS last updated on 15/Apr/18

sorry somehow I thought it was

x^{3} \dots I might need new glasses; -)

anyway your answer is right

Commented by Rasheed.Sindhi last updated on 16/Apr/18

What is the use of [\frac{α + β}{α β}] \times α β ?