If the cubic equation $a^3 – 4a^2 + 5a – 2 = 0 $ has the root x, y, z then find the value of x + y + z.

If the cubic equation $a^3 – 4a^2 + 5a – 2 = 0 $ has the root x, y, z then find the value of x + y + z.
यदि घन समीकरण $a^3 – 4a^2 + 5a – 2 = 0 $ का मूल x, y, z है तो x +y +z का मान ज्ञात कीजिए।

5 6 7 4

Detailed Solution & Logic

Correct Answer:

4

Solution:
For the cubic equation,
$ a^3-4a^2+5a-2=0 $
By Vieta's formula, for
$ ax^3+bx^2+cx+d=0, $
the sum of the roots is
$x+y+z=-\dfrac{b}{a}. $
Here,
$ a=1,\quad b=-4. $
Therefore,
$ x+y+z=-\dfrac{-4}{1}=4. $
x+y+z=4

Answer: 4 ✅

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