Question

the value of k if x - 1 is a factor
of 4x2+5x+k
OA) 9
O B)-9
O C) 5
OD)-5​

Answer 1

Given :

• x - 1 is a factor of 4x² + 5x + k

To find :

• The value of k

Solution :

→ Here, we are given a polynomial and it's factor and we have to find the value of k. So, by substituting the value of x in the polynomial we will get the value of k.

Let's do it!

→ p (x) = 4x² + 5x + k

→ x - 1 is a factor

→ x - 1 = 0

→ x = 1

→ The value of x = 1

→ p (x) = 4(1)² + 5(1) + k = 0

→ 4(1) + 5 + k = 0

→ 4 + 5 + k = 0

→ 9 + k = 0

→ k = - 9

→ Therefore, the value of k = - 9

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Let's verify :-

To verify the value of k substitute the value of x and k in the polynomial if the resultant value will be zero then the value of k is right.

→ 4x² + 5x + k = 0

Taking LHS :

→ 4(1)² + 5(1) + (-9)

→ 4 + 5 - 9

→ 9 - 9

→ 0

LHS = 0

RHS = 0

LHS = RHS

Hence, verified!