Question

The unknown coefficient of the equation x^2 +bx+3=0 is determined by throwing an ordinary six faced die. The probability of that equation has real roots is

Answer 1

Answer:

sorry

I don't know plz sorry

Answer 2

Answer:

The probability of getting that equation has real roots is $\frac{1}{2}$.

Step-by-step explanation:

For a quadratic equation, $ax^2+bx+c=0$, the expression $b^2-4ac$ is called the discriminant.

If the value of discriminant $b^2-4ac > 0$, then the quadratic equation has two distinct real roots.

If the value of discriminant $b^2-4ac =0$, then the quadratic equation has repeated real roots.

Consider the quadratic equation as follows:

$x^2+bx+3=0$ ...... (1)

Here, $a=1$, $b=b$ and $c=3$

Then discriminant is

$b^2-4ac=b^2-4(1)(3)$

             $=b^2-12$

A die is thrown. Then sample will be

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

According to the question, probability that the equation (1) has real root

So, either $b^2-12=0$ or $b^2-12 > 0$.

Case1. If $b^2-12=0$.

⇒ $b^2=12$

⇒ $b=2\sqrt{3}$, which is not possible.

As $2\sqrt{3}$ is not in the sample space.

Case2. If $b^2-12 > 0$.

⇒ $b^2 > 12$

Then, for $b=4,5,6$.The expression $b^2 > 12$ holds.

Thus, probability of getting real roots = $\frac{3}{6}$

                                                                = $\frac{1}{2}$.

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