Question

if -1 is a zero of the polynomial p (x) = ax^3-x^2+x+4, find the value of the a

Answer 1

Answer:

a = 2

Step-by-step explanation:

If -1 is a zero of p(x) then p(x) must be equal to 0.

So, putting the values,

→a×(-1)³-(-1)²+(-1)+4=0

→a×(-1)-1-1+4=0

→-a+2=0

→-a=-2

→a=2

Hence required value of a is 2.

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Answer 2

The polynomial given is :

• ax³ - x² + x + 4

The zero of the given polynomial is :

• - 1

Substituting x = - 1 in the polynomial and finding the value of a :

• ax³ - x² + x + 4 = 0
• a (- 1)³ - (- 1)² + (- 1) + 4 = 0
• a (- 1) - (1) - 1 + 4 = 0
• - a - 1 - 1 + 4 = 0
• - a - 2 + 4 = 0
• - a + 2 = 0
• - a = - 2
• a = 2

Therefore, the value of a is 2 in the polynomial ax³ - x² + x + 4 when - 1 is the zero.

V E R I F I C A T I O N :

Substituting a = 2 and x = - 1 and verifying whether the value satisfies the polynomial or not :

• ax³ - x² + x + 4 = 0
• (2) (- 1)³ - (- 1)² + (- 1) + 4 = 0
• 2 (- 1) - (1) - 1 + 4 = 0
• - 2 - 1 - 1 + 4 = 0
• - 2 - 2 + 4 = 0
• - 4 + 4 = 0
• 0 = 0
• LHS = RHS

H E N C E, V E R I F I E D!