Q79 / 160 · TS EAMCET 2020 (14 Sep Shift 1) · Mathematics

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

  • A
    $\frac{1}{6}$
  • Correct answer
    B
    $\frac{5}{6}$
  • C
    $\frac{3}{4}$
  • D
    $\frac{7}{12}$

Solution

Given equation, $x^2+a x+b$ has real roots if $a^2 \geq 4 b$ favourable outcomes is $\begin{aligned} & (3,1)(3,2)(4,1)(4,2)(4,3),(4,4) \\ & (5,1)(5,2)(5,3)(5,4) \\ & \therefore \text { Required probability }=\frac{10}{3 \times 4}=\frac{10}{12}=\frac{5}{6} \end{aligned}$

Hence, the correct answer is option: 'B'.

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