Question

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

Answer 1

$\large{\underline{\bf{\purple{Correct\:Question:-}}}}$

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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$\large{\underline{\bf{\green{Given:-}}}}$

✰ p(x) = ax² - 13x - b

✰ factors are x -1 and x +3

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the Value of a and b.

$\huge{\underline{\bf{\red{Solution:-}}}}$

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

$: \mapsto \sf\:1+(-3)= \frac{-(-13)}{a}$

$: \mapsto \sf\:-2 = \frac{13}{a}$

$: \mapsto \sf\: - 2a =13$

$: \mapsto \sf\:a =\frac{-13}{2}$

product of zeroes (αβ) = c/a

$: \mapsto \sf\:1\times(-3)= \frac{ \frac{ - b}{ - 13} }{2} \\ \\ : \mapsto \sf \: - 3 = \frac{2b}{13} \\ \\: \mapsto \sf - 39 = 2b \\ \\ : \mapsto \sf \: b = \frac{ - 39}{2}$

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Answer 2

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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