Question

x-3 and x+3 are the factors of 4x^3+ax^2+bx. find the value of a and b ​

Answer 1

Given:-

• f(x) = (x - 3) & (x + 3)

• P(x) = 4x³ + ax² + bx

To Find:-

• The Value of a and b

Now,

→ f(x) = x -3 = 0

→ x = 3

Put the value of x in P(x)

→ P(x) = 4x³ + ax² + bx

→ P(3) = 4(3)³ + a(3)² + b(3) = 0

→ 108 + 9a + 3b = 0

→ 9a + 3b = -108

→ 3 (3a + b) = -36

→ 3a + b = -36.......Eq1

Again,

→ f(x) = x + 3 = 0

→ x = -3

Put the value of x in P(x)

→ P(x) = 4x³ + ax² + bx

→ P(-3) = 4(-3)³ + a(-3)² + b(-3) = 0

→ -108 + 9a -3b = 0

→ 9a - 3b = 108

→ 3( 3a - b ) = 36

→ 3a - b = 36.......Eq2

Subtracting the equation 1 and 2

→ 3a + b -(3a - b ) = -36 - 36

→ 3a + b - 3a + b = -72

→ 2b = -72

→ b = -72/2

→ b = -36

Now, Putting the value of b in eq 2

→ 3a - b = 36

→ 3a - (-36) = 36

→ 3a + 36 = 36

→ 3a = 36 - 36

→ 3a = 0

→ a = 0/3

→ a = 0

Hence, The Value of a and b is 0 and -36 respectively.