two numbers b and c are chosen at random with replacement from the numbers 1,2,3,4,5,6,7,8,9 .find the probability that x²+bx+c>0 for all x belongs to R.

Open in App

Solution

dear student

$t w o n u m b e r s a r e c h o s e n w i t h r e p l a c e m e n t n u m b e r o f w a y s = {}_{1}^{10}C \times {}_{1}^{10}C = 100 x^{2} + b x + c > 0 a l w a y s p o s i t i v e s o D < 0 b^{2} - 4 c < 0 f o r b = 1, c c a n t a k e v a l u e s 1 t o 9, 9 c a s e s f o r b = 2, c c a n t a k e v a l u e s 2 t o 9, 8 c a s e s f o r b = 3, c c a n t a k e v a l u e s 3 t o 9, 7 c a s e s f o r b = 4, c c a n t a k e v a l u e s 5 t o 9, 5 c a s e s f o r b = 5, c c a n t a k e v a l u e s 7 t o 9, 3 c a s e s f o r b = 6 - 9, c c a n t a k e n o v a l u e s s u c h t h a t D < 0 t o t a l c a s e s = 32 p r o b a b i l i t y = \frac{32}{100}$

regards

Suggest Corrections

Similar questions

b

c

1, 2, 3, 4, 5, 6, 7, 8, 9)

x^{2} + b x + c > 0 \forall x ϵ R

b

c

1, 2, 3, 4, 5, 6, 7, 8

9

x^{2} + b x + c > 0

x \in R

\frac{4 k}{81}

k

x^{2} + b x + c > 0

x \in R

x^{2} + b x + c > 0

x ϵ R

a, b, c

a x^{2} + b x + c = 0

S = 1, 2, 3, 4, 5, 6

Join BYJU'S Learning Program