Question

two engineers go for interview for two vacancy in the same grade.the probability of engineer 1 getting selected is 1/3 and that of engineer 2 is 1/5 . find the probability that only


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Answer 1

Answer:

EXPLANATION.

Quadratic equation.

⇒ x² - (k + 6)x + 2(2k - 1) = 0.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -[-(k + 6)]/1 = (k + 6).

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 2(2k - 1)/1 = 2(2k - 1).

Sum of the roots of the equation is equal to half of their products.

⇒ (α + β) = 1/2 x (αβ).

⇒ (k + 6) = 1/2 x [2(2k - 1)].

⇒ 2(k + 6) = 2(2k - 1).

⇒ 2k + 12 = 4k - 2.

⇒ 2k + 12 - 4k + 2 = 0.

⇒ - 2k + 14 = 0.

⇒ 2k = 14.

⇒ k = 7.

                                                                                                                           

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.