Question

if x2-3x+2 is a factor of x4-ax2+b=0 then the respective values of a and b

Answer 1

Answer:

a = 15/7, b = 8/7

Step-by-step explanation:

Factors of x² - 3x + 2 = (x - 2)(x - 1)

Since x² - 3x + 2 is factor of x⁴ - ax²+ b = 0, substituting the values of x in the equation x⁴ - ax²+ b = 0 should also satisfy the equation.

For x = 1,

(1)⁴ - a(1)³ + b = 0

a - b = 1 ===========> Equation 1

For x = 2,

(2)⁴ - a(2)³ + b = 0

16 - 8a + b = 0

8a -  b = 16 ==============> Equation 2

Solve Equation 1 and Equation 2:

8a - b =  16

 a - b =   1

-    +      -

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7a = 15 => a = 15/7

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Substitute value of a in equation 1.

a -b = 1

=> 15/7 - b = 1

=> b = 15/7 - 1 = 8/7.