CAT Exam Model Paper 5 with solutions for free online practice

Question : 15 of 60

Marks: +1, -0

When ‘2’ is added to each of the three roots of x

^{3}

- Ax

^{2}

+ Bx - C = 0, we get the roots of x

^{3}

+ Px

^{2 }

+ Qx - 18 = 0. A, B, C, P and Q are all non- zero real numbers. W hat is the value of (4A + 2B + C)?

Solution:

Let the roots of the equation x

^{3}

- Ax

^{2}

+ Bx - C = 0 be α, β,γ respectively.
So the roots ofx

^{3}

+ Px

^{2 }

+ Qx - 18 = 0 will be αx + 2, β + 2,γ+ 2.
(α + 2 )(β + 2 )(γ + 2) = 18
4 (α + β + γ) + 2( αβ + βγ + γα ) + αβγ + 8 = 18
⇒ 4A + 2B + C = 10

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