Question

if0 and 1 are the zeroes of the polynomial S(x) = 2x^3 - 3x^2 + ax + b, find the values
of a and b.​

Answer 1

EXPLANATION.

→ 0 and 1 are the zeroes of the polynomial

s(x) = 2x³ - 3x² + ax + b,

→ To find the value of a and b.

→ Case = 1.

→ put the value of x = 0 in equation

→ s(0) = 2(0)³ - 3(0)² + a(0) + b = 0

→ s(0) = 0 - 0 + 0 + b = 0

→ s(0) = b = 0 ..... (1)

→ Case = 2.

→ put the value of x = 1 in equation

→ s(1) = 2(1)³ - 3(1)² + a(1) + b = 0

→ s(1) = 2 - 3 + a + b = 0

→ s(1) = -1 + a + b = 0

→ s(1) = a + b = 1 .......(2)

→ put the value of equation (1) in (2)

we get,

→ a + 0 = 1

→ a = 1

→ Therefore, value of a = 1 and b = 0.

Answer 2

Step-by-step explanation:

Given : -

• the zeroes of the polynomial S(x) = 2x^3 - 3x^2 + ax + b,

.To Find : -

• find the values of a and b.

Solution : -

f(0) = 0 and f(1) = 0

✪ substitute all values :✪

➻ f(0) = 2(0)³ - 3(0)² + a(0) + b = 0

➻ b = 0.......(1)

f(1) = 2(1)³ - 3(1)² + a(1) + b = 0

✪ Substitute all values :✪

➻ 2 - 3 + a + b = 0

➻ a + b - 1 = 0

➻ a + b = 1 ........(2)

from equations (1) and (2),

a + b = 1

b = 0

________

a = 1

hence, value of a = 1 and b = 0