Question

if one root (zero) of the polynomial x²+5x+k is the raciprocal of the other .find k​

Answer 1

AnsWer :

k = 1.

GiveN :

• If one root (zero) of the polynomial x²+5x+k is the raciprocal of the other.

To FinD :

The value of k.

SolutioN :

We have, Polynomial.

→ x² + 5x + k.

☯ Compare With General Expression.

ax² + bx + c

Where as,

• a = 1.
• b = 5.
• c = k.

☛ Let,

• The Zero of polynomial be a and b.
• According to Condition b = 1 / a.
• a , 1 / a are the two Zero of polynomial.

✎ Sum of Zeros.

→ a + b = - b/ a.

$\rule{90}2$

✎ Product Of Zeros.

a * b = c / a.

So,

→ a * 1 / a = k / 1.

→ 1 = k.

→ K = 1.

✡ Therefore the value of k is 1.

Answer 2

Step-by-step explanation:

QUESTION:-

if one root (zero) of the polynomial x²+5x+k is the raciprocal of the other .find k

ANSWER:-

We have, Polynomial.

→ x² + 5x + k.

☯ Compare With General Expression.

ax² + bx + c

Where as,

a = 1.

b = 5.

c = k.

☛ Let,

The Zero of polynomial be a and b.

According to Condition b = 1 / a.

a , 1 / a are the two Zero of polynomial.

✎ Sum of Zeros.

→ a + b = - b/ a.

✎ Product Of Zeros.

a * b = c / a.

So,

→ a * 1 / a = k / 1.

→ 1 = k.

→ K = 1.

✡ Therefore the value of k is 1.