If two zeros of the polynomial fx - x3 -4x2 - 3x-12 are -3 and -3- then find its third zero- -2 MARKS-

Concept : 1 Mark Application : 1 Mark Let α = √(3), β = √(3) be the given zeros and γ be the third zero. Then, α +β +γ = ( 4/1 ) [ Using α +β +γ = b/a ] ...

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Standard IX

Mathematics

Zeros of a polynomial

If two zeros ...

Question

If two zeros of the polynomial $f (x) = x^{3} - 4 x^{2} - 3 x + 12$ are $\sqrt{3}$ and $- \sqrt{3}$ , then find its third zero. [2 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark

Let $α = \sqrt{3}, β = - \sqrt{3}$ be the given zeros and $γ$ be the third zero. Then,

$α + β + γ = - (\frac{- 4}{1})$ $[U s i n g α + β + γ = - \frac{b}{a}]$

$\Rightarrow \sqrt{3} - \sqrt{3} + γ = 4$

$\Rightarrow γ = 4$

Hence, third zero is 4.

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If two zeros of the polynomial f(x)=x3−4x2−3x+12 are √3 and −√3, then find its third zero. [2 MARKS]

Concept : 1 Mark Application : 1 Mark Let α=√3,β=−√3 be the given zeros and γ be the third zero. Then, α+β+γ=−(−41) [Using α+β+γ=−ba] ⇒√3−√3+γ=4 ⇒γ=4 Hence, third zero is 4.

If two zeros of the polynomial $f (x) = x^{3} - 4 x^{2} - 3 x + 12$ are $\sqrt{3}$ and $- \sqrt{3}$ , then find its third zero. [2 MARKS]

Concept : 1 Mark
Application : 1 Mark

Let $α = \sqrt{3}, β = - \sqrt{3}$ be the given zeros and $γ$ be the third zero. Then,

$α + β + γ = - (\frac{- 4}{1})$ $[U s i n g α + β + γ = - \frac{b}{a}]$

$\Rightarrow \sqrt{3} - \sqrt{3} + γ = 4$

$\Rightarrow γ = 4$

Hence, third zero is 4.