Question

if 2 and -3 are the zeros of the polynomial x*3 + ax*2 +bx - 12 , find the values of a and b​

Answer 1

Solution

Given :-

• Polynomial , x³ + ax² + bx -12 = 0
• 2 & -3 are roots this Equation

Find :-

• Value of a & b

Explanation

We know,

Here, 2 & -3 are roots this Equation that's means these are satisfied sm quadratic equations.

Case 1.

• When, x = 2

==> 2³ + a (2)² + 2b - 12 = 0

==> 8 + 4a + 2b - 12 = 0

==> 4a + 2b = 12 - 8

==> 2(2a + b) = 4

==> 2a + b = 4/2

==> 2a + b = 2 __________(1)

Case 2.

• when, x = -3

==> (-3)³ + a(-3)² + b(-3) - 12 = 0

==> -27 + 9a - 3b = 12

==> 3(3a - b) = 12 + 27

==> 3a - b = 39/3

==> 3a - b = 13_________(2)

add equ(1) & equ(2)

==> 5a = 15

==> a = 15/5

==> a = 5

Keep in equ(2)

==> 3×5 - b = 13

==> b = -13 + 15

==> b = 2

Hence

• Value of a be = 5
• Value of b = 2

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