Question

39. Ifm is a natural number such that m = 5, then the probability that the quadratic equation 2x^2 + 2mx +
m + 1 = 0 has real roots IS:-
a.1/5
b.2/3
c.1/5
d.3/5
​

Answer 1

Answer:

Probability = 3/5  

Step-by-step explanation:

2x^2 + 2mx + m + 1 = 0

if  (2m)²  ≥  4(2)(m+1)

if 4m²  ≥  4(2)(m+1)

if m²  ≥  (2)(m+1)

if m²  ≥  2m+ 2

if m² - 2m ≥ 2

if m² - 2m + 1 ≥ 2 + 1

if (m - 1)² ≥ 3

if  m - 1 ≥ √3

if  m  ≥ √3 + 1

if  m  ≥  2.732

for m from 1 to 5

m = 3 , 4  ,5  will have real roots

=> Probability = 3/5