Question

1 point) If a is uniformly distributed over [−27,23], what is the probability that the roots of the equation x2+ax+a+80=0 are both real?

(1 point) If a is uniformly distributed over [-27, 23), what is the probability that the roots of the equation r+ ax + a + 80 = 0 are both real?

Answer 1

# le. is uniformly distributed over [-27, 23] distribution of a is fca 15 -27 < a <23 otherwise Now x²+an +a+80=0 has real roots if its discriminant is non negative a- 4 (9+80) 20 a²_ 4 a - 320 7,0 la-20) (0+16) > 0 or as-16 a>,20 20 le it a>,20 ak-16 then both roots of given equation dise seal Probability that both roots are real Pa>, 20 or a< -16) - 16 123 to I dx + I da si 50 50 -27 20

Hol 12+ [*1.5) 5o ((-16+27) + (23-20) ) 5o ( 11 + 3) 11 14 - So, Probability that the both roots of equation real is 11/15