Question

If one of the zero of polynomial 3x²+5x+k is -1, then find out the value of k.​

Answer 1

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

• p(x) = 3x² + 5x + k
• given zero = -1

$\large\bf\underline {To \: find:-}$

• Value of k

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

• p(x) = 3x² + 5x + k
• given zero = -1
• So, x = -1

✝️ Putting value of x = -1 in the given polynomial.

⠀⠀⠀⠀⠀⠀⠀⠀»» 3x² + 5x + k = 0

⠀⠀⠀⠀⠀⠀⠀⠀»» 3(-1)² + 5(-1) + k = 0

⠀⠀⠀⠀⠀⠀⠀⠀»» 3 × 1 - 5 + k = 0

⠀⠀⠀⠀⠀⠀⠀⠀»» 3 - 5 + k = 0

⠀⠀⠀⠀⠀⠀⠀⠀»» -2 + k = 0

⠀⠀⠀⠀⠀⠀⠀⠀»★ k = 2

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✝️ $\large\underline{ \bf \: verification : - }$

• p(x) = 3x² + 5x + k

putting value k = 2 in the given polynomial

➝ 3x² + 5x + 2

Now finding zeroes of polynomial 3x² + 5x + 2

➝ 3x² + 3x + 2x + 2

➝ 3x(x + 1) + 2(x + 1)

➝ (3x + 2)(x + 1)

• ➝ x = -2/3 or x = -1

»★ So, we get the same zero x = -1 that is given in the question so value of k = 2 is correct.

hence , Verified.

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Answer 2

Answer:-

$\sf{The \ value \ of \ k \ is \ 2.}$

Given:

• The given polynomial is $\sf{3x^{2}+5x+k}$

• One of the zero of the polynomial is -1.

To find:

• The value of k.

Solution:

$\sf{Substitute \ x=(-1) \ in \ given \ polynomial. }$

$\sf{\implies{3(-1)^{2}+5(-1)+k=0}}$

$\sf{\implies{3-5+k=0}}$

$\sf{\implies{-2+k=0}}$

$\boxed{\sf{\implies{k=2}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ k \ is \ 2.}}}$

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$\sf\blue{\underline{\underline{Verification:}}}$

$\sf{\implies{3x^{2}+5x+2}}$

$\sf{\implies{3x^{2}+3x+2x+2}}$

$\sf{\implies{3x(x+1)+2(x+1)}}$

$\sf{\implies{(x+1)(3x+2)}}$

$\sf{\implies{(x+1)=0 \ or \ (3x+2)=0}}$

$\sf{\implies{x=-1 \ or \ x=\frac{-2}{3}}}$