Question

if the sum of the zeros of polynomial F (X equal to x cube minus 3 X square + 4 x minus 5 is 6 then value of k is​

Answer 1

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CORRECT QUESTION -

If the sum of the Zeroes of the polynomial

$=> F(x) = { x } ^ 3 - 3 k{ x } ^ 2 + 4x - 5$

$\sf{ Sum \: Of \: Zeroes \: = \: \alpha + \beta = \dfrac{ -b}{ a } }$

HERE -

A CubIc Equation can Be Written As :

$A { x } ^ 3 + B { x } ^ 2 + Cx + D = 0$

CompAriNg ThE CoEffiCiEnTs -

$\tt{ A = 1 } \\ \\ \tt{ B = -3k } \\ \\ \tt { C = 4 } \\ \\ \tt{ D = -5 }$

SuM Of ZerOes :

The Zeroes Of a CubIc Polynomial are AlPha , BetA , and GaMmA

$\sf{ Sum \: Of \: Zeroes \: = \: \alpha + \beta + \gamma = \dfrac{ -b}{ a } }$

SubStuTinG ThE ReqUiRed ValUes -

$\sf{ Sum \: Of \: Zeroes \: = 3k }$

$\mathfrak { => -3k = -6 } \\ \\ \sf{ k = 2 ........... [ A ] }$

So, the required Value Of K = 2.

ANSWER -

the required Value Of K = 2.

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ADDITIONAL FORMULAE -

• $\alpha + \beta + \gamma = \dfrac{ -b}{ a }$

• $\alpha \beta + \beta \gamma + \alpha \gamma = \dfrac{ c}{ a }$

• $\alpha \beta \gamma = \dfrac{ d }{ a }$

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Answer 2

Correct question :-

If the sum of the zeroes of the polynomial f(x) = x³ - 3kx² + 4x - 5 is 6 is 5, then the value of k is ____

Given :-

Sum of the zeros of polynomial f(x) = x³ - 3kx² + 4x - 5 is 6.

i.e. α + β + γ = 6.

To find :-

The value of 'k'.

Solution :-

We know, sum of the zeros of a cubic polynomial(ax³ + bx² + c + d)           = minus of coefficient of  x²/coefficient of x³

= -b/a

Now, the given polynomial is x³ - 3x² + 4x - 5 is 6.

A/q, α + β + γ = 6

⇒-b/a = 6

⇒ -(-3k)/1 = 6

⇒3k = 6

⇒k = 6/3

⇒k = 2

∴ So, the value of k for which the sum of the zeros of the polynomial f(x) is 6, is 2.