Question

(4) If the sum of zeroes of the polynomial p(x) = (k - 14)x² - 2x – 12x is 1, and
the value of k.
A)-14 B) C) 16 D)-12
11.​

Answer 1

Answer:

The values of k are -4 and 46

Step-by-step explanation:

The given polynomial is (k^2-14)x^2-2x-12(k

2

−14)x

2

−2x−12

The sum of zeros of a quadratic equation is -\frac{b}{a}−

a

b

Hence, the sum of the zeros of the given quadratic is

\begin{lgathered}-\frac{-2}{(k^2-14}\\\\\frac{2}{(k^2-14}\end{lgathered}

−

(k

2

−14

−2

(k

2

−14

2

Now, from the given directions, this expression should be equal to 1.

\begin{lgathered}\frac{2}{(k^2-14}=1\\\\k^2-14=2\\\\k^2=16\\\\k=\pm\sqrt{16}\\\\k=\pm4\end{lgathered}

(k

2

−14

2

=1

k

2

−14=2

k

2

=16

k=±

16

k=±4