Question

24
3. If one zero of the quadratic polynomial x2+3x+k is 2, then the value of k is
a) 10
b) -10
c) 5
d) -5
​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{one zero of}\;\mathsf{x^2+3x+k}\;\textsf{is 2}$

$\underline{\textsf{To find:}}$

$\textsf{The value of k}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the other zero be "m"}$

$\textsf{Then,}$

$\textsf{Sum of the zeros}\,\mathsf{=\dfrac{-b}{a}}$

$\implies\mathsf{2+m=\dfrac{-3}{1}}$

$\implies\mathsf{2+m=-3}$

$\implies\mathsf{m=-3-2}$

$\implies\mathsf{m=-5}$

$\therefore\textsf{The other zero is -5}$

$\textsf{Also,}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{c}{a}}$

$\implies\mathsf{2{\times}m=\dfrac{k}{1}}$

$\implies\mathsf{2{\times}(-5)=\dfrac{k}{1}}$

$\implies\boxed{\mathsf{k=-10}}$

$\underline{\textsf{Answer:}}$

$\textsf{Opion (b) is correct}$

Answer 2

SOLUTION

GIVEN

$\sf{}one \: zero \: of \: the \: quadratic \: polynomial \: \: {x}^{2} + 3x + k$

TO DETERMINE

The value of k

EVALUATION

$\sf{}f(x) = {x}^{2} + 3x + k$

It is given that

$\sf{}one \: zero \: of \: the \: quadratic \: polynomial \: \: {x}^{2} + 3x + k$

So

$\sf{}f(2) = 0$

$\implies \sf{} {(2)}^{2} + (3 \times 2) + k = 0$

$\implies \sf{} 4 + 6 + k = 0$

$\implies \sf{} k + 10 = 0$

$\implies \sf{} k = - 10$

FINAL ANSWER

Hence the required value of k is - 10

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