Question

if 2 is a zero of the cubic polynomial, x³- x² + ax + 4, then find the value of a.​

Answer 1

GIVEN:

Cubic Polynomial = x³- x² + ax + 4

One of the zeroes of polynomial = 2

TO FIND:

The value of 'a'

SOLUTION:

We know that,

The value of p(x) = x³- x² + ax + 4 is 0. So, when we substitute zeroes in the polynomial the value of polynomial will be zero.

p(2) = x³- x² + ax + 4

= (2)³ - (2)² + a(2) + 4

= 8 - 4 + 2a + 4

= 12 - 4 + 2a

= 8 + 2a

a = -8/2

a = -4

Therefore, the value of a is -4.

VERIFICATION:

Substitute a = -4 in the polynomial. Then the value will be 0.

p(2) = x³- x² + ax + 4

= (2)³ - (2)² + (-4)(2) + 4

= 8 - 4 - 8 + 4

= 0

Hence, verified!

Answer 2

Step-by-step explanation:

GIVEN:

Cubic Polynomial = x³- x² + ax + 4

One of the zeroes of polynomial = 2

TO FIND:

The value of 'a'

SOLUTION:

We know that,

The value of p(x) = x³- x² + ax + 4 is 0. So, when we substitute zeroes in the polynomial the value of polynomial will be zero.

p(2) = x³- x² + ax + 4

= (2)³ - (2)² + a(2) + 4

= 8 - 4 + 2a + 4

= 12 - 4 + 2a

= 8 + 2a

a = -8/2

a = -4

Therefore, the value of a is -4.

VERIFICATION:

Substitute a = -4 in the polynomial. Then the value will be 0.

p(2) = x³- x² + ax + 4

= (2)³ - (2)² + (-4)(2) + 4

= 8 - 4 - 8 + 4

= 0

Hence, verified!

hope this helps you!!