Probable Real Quadratika.

Probability Level 4

The values of $a \ \text{and} \ b$ are equally possible in the square $|a| \leq 1, |b| \leq 1$ . Find the probability (up to 3 decimal points) that the roots of the quadratic trinomial $(x^2+2ax+b)$ are real.

Practice the set Target JEE_Advanced - 2015 and boost up your preparation.

The answer is 0.667.

1 solution

Shubham Garg
Jun 29, 2015

Let the values of $a$ be represented on $x$ and $b$ on $y$ axes respectively.

the area of square formed by condition given is 4 $(2×2)$ . $(|x| \leq 1 ,|y| \leq 1)$

For the roots to be real $a^2-b \geq 0$ $\Rightarrow x^2 \geq y$

the area bounded by parabola and square (outside the parabola) is $\frac 8 3$ .

This is the favourable area.

$Probability = \frac{favourable \quad area}{total \quad area}=\frac {\frac 8 3 }{4} =\boxed { \frac 2 3}$

Probable Real Quadratika.

Practice the set Target JEE_Advanced - 2015 and boost up your preparation.

The answer is 0.667.

1 solution

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