Math, asked by saranjeetkaur918, 10 months ago

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

Answered by Anonymous
4

\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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Answered by Anonymous
1

CorrectQuestion:−

If x -1 and x + 3 are factors of polynomial ax² - 13x - b Then find the Value of a and b.

━━━━━━━━━━━━━━━━━━━━━━━

\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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