If X -1 and X +3 are factors of the polynomial X cube minus a X square -13 X minus B then find the value of if X -1 and X +3Are the factors of the polynomial X cube minus a X square -13 X minus B then find the values of a and B
Answers
If x -1 and x + 3 are factors of polynomial ax² - 13x - b Then find the Value of a and b.
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✰ p(x) = ax² - 13x - b
✰ factors are x -1 and x +3
✰ we need to find the Value of a and b.
we know that x -1 and x +3 are the factors of polynomial ax² - 13x - b
Then
x = 1 or x = -3
Let α and β are the zeroes of the given polynomial.
Let α = 1
and β = -3
and ,
- a = a
- b = -13
- c = -b
Now,
Sum of zeroes (α + β) = - b/a
product of zeroes (αβ) = c/a
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CorrectQuestion:−
If x -1 and x + 3 are factors of polynomial ax² - 13x - b Then find the Value of a and b.
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\large{\underline{\bf{\green{Given:-}}}}
Given:−
✰ p(x) = ax² - 13x - b
✰ factors are x -1 and x +3
\large{\underline{\bf{\green{To\:Find:-}}}}
ToFind:−
✰ we need to find the Value of a and b.
\huge{\underline{\bf{\red{Solution:-}}}}
Solution:−
we know that x -1 and x +3 are the factors of polynomial ax² - 13x - b
Then
\hookrightarrow \sf\:↪ x = 1 or x = -3
Let α and β are the zeroes of the given polynomial.
Let α = 1
and β = -3
and ,
a = a
b = -13
c = -b
Now,
Sum of zeroes (α + β) = - b/a
: \mapsto \sf\:1+(-3)= \frac{-(-13)}{a}:↦1+(−3)=
a
−(−13)
: \mapsto \sf\:-2 = \frac{13}{a}:↦−2=
a
13
: \mapsto \sf\: - 2a =13:↦−2a=13
: \mapsto \sf\:a =\frac{-13}{2}:↦a=
2
−13
product of zeroes (αβ) = c/a
\begin{lgathered}: \mapsto \sf\:1\times(-3)= \frac{ \frac{ - b}{ - 13} }{2} \\ \\ : \mapsto \sf \: - 3 = \frac{2b}{13} \\ \\: \mapsto \sf - 39 = 2b \\ \\ : \mapsto \sf \: b = \frac{ - 39}{2}\end{lgathered}
:↦1×(−3)=
2
−13
−b
:↦−3=
13
2b
:↦−39=2b
:↦b=
2
−39
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