Question

If X=-1 and x=3 are the roots for the equation x^2+ax+b=0, find the value of a and b.
Guys help me please.

Answer 1

Given :

• p (x) = x² + ax + b = 0

• The roots for this equation are -1 and 3

To find :

• The value of a and b

Solution :

→ p (x) = x² + ax + b = 0

→ p (-1) = (-1)² + a(-1) + b = 0

→ 1 - a + b = 0

→ - a + b = - 1

→ - (a - b) = - 1

→ a - b = 1

Equation (1) :→ a - b = 1

→ p (x) = x² + ax + b = 0

→ p (3) = (3)² + a(3) + b = 0

→ 9 + 3a + b = 0

→ 3a + b = - 9

Equation (2) :→ 3a + b = - 9

Solving equation (1) and (2) :-

→ a - b = 1

→ 3a + b = - 9

___________

4a ⠀⠀⠀= - 8

___________

→ 4a = - 8

→ a = - 8 ÷ 4

→ a = - 2

The value of a = - 2

Substitute the value of a in equation (1) :-

→ a - b = 1

→ - 2 - b = 1

→ - b = 1 + 2

→ - b = 3

→ b = - 3

The value of b = - 3

Therefore, the value of a = - 2 and b = - 3