If the coefficients a and b of a quadratic ex | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The quadratic equation $x^2+ax+b=0$ has real roots if the discriminant $D = a^2 - 4b \geq 0$, which implies $a^2 \geq 4b$.Given $a \in \{3, 4, 5\}

Vedclass · Accepted Answer

$\frac{5}{6}$

Vedclass · Answer

(B) The quadratic equation $x^2+ax+b=0$ has real roots if the discriminant $D = a^2 - 4b \geq 0$, which implies $a^2 \geq 4b$.Given $a \in \{3, 4, 5\}$ and $b \in \{1, 2, 3, 4\}$, the total number of possible pairs $(a, b)$ is $3 	imes 4 = 12$.We check the condition $a^2 \geq 4b$ for each pair:If $a=3$, $a^2=9$: $9 \geq 4b \implies b \leq 2.25$. Possible values for $b$ are $1, 2$ ($2$ pairs).If $a=4$, $a^2=16$: $16 \geq 4b \implies b \leq 4$. Possible values for $b$ are $1, 2, 3, 4$ ($4$ pairs).If $a=5$, $a^2=25$: $25 \geq 4b \implies b \leq 6.25$. Possible values for $b$ are $1, 2, 3, 4$ ($4$ pairs).Total favorable outcomes = $2 + 4 + 4 = 10$.Therefore, the required probability is $\frac{10}{12} = \frac{5}{6}$.

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

Similar Questions

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw a sum of $9$ with both dice will be awarded the prize. If $A$ throws first,then the probability that $B$ wins the game is

If $3$ numbers are chosen from the first $15$ natural numbers,what is the probability that the numbers are in arithmetic progression?

Two numbers are selected at random from $40$ consecutive natural numbers. What is the probability that the sum of the numbers is odd?

If two cards are drawn at random simultaneously from a well-shuffled pack of $52$ playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of $3$ is

$A$ box contains $12$ balls,of which $4$ are red,$5$ are green,and $3$ are white. If $3$ balls are drawn at random simultaneously from the box,then the probability that exactly $2$ balls have the same colour is

Vedclass Test Series

Exam Paper Generator

Online Exam Module