Question

Value of k if 5 is zero of polynomial p(x) = 4 x³ – 16x² + kx – 5 is​

Answer 1

Answer:

f(x)=f(x)=x

4

−x

3

−8x

2

+kx+12

If 3 is the zero of f(x),then,

f(3)=0

=3

4

−3

3

−8(3)

2

+k(3)+12

=81−27−72+3k+12

=93−99+3k

=>3k=6

=>k=2

Answer 2

Given :–

• A polynomial, p(x) = 4x³ – 16x² + kx – 5.
• 5 is zero of the given polynomial.

To Find :–

• Value of k.

Solution :–

Given,

5 is zero of the given polynomial, 4x³ – 16x² + kx – 5.

So,

• x + 5 = 0

• x = –5

Now, put the value of x in the given polynomial.

→ 4x³ – 16x² + kx – 5

→ 4(–5)³ – 16(–5)² + k(–5) – 5

→ 4(–125) – 16(25) + k(–5) – 5

Now, open all the brackets,

→ –500 – 400 – 5k – 5

→ –900 – 5k = 5

→ –5k = 5 + 900

→ –5k = 905

→ k = $\dfrac{\cancel{905}}{\cancel{-5}}$

→ k = –181

Hence,

The value of k is –181.

Check :–

5 is zero of the given polynomial.

→ x + 5 = 0

• x = –5
• k = –181

Now, put both the values of x and k in the given polynomial.

→ 4x³ – 16x² + kx – 5

→ 4(–5)³ – 16(–5)² + (–181)(–5) – 5

→ 4(–125) – 16(25) + (905) – 5

Now, open all the three brackets.

→ –500 – 400 + 905 – 5

→ –900 + 900

→ 0

Since, the answer is zero.

So, the value of k is correct.