Question

If x²-4x+3=0, then what is the value of (x³+4x²+7x+24)(x²+2x+3)^-1?

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The Correct Option is C

The correct option is (C): 6.
x² - 4x + 3 = 0
x² = 4x - 3...(i)
Now, (x³ + 4x² + 7x + 24)(x² + 2x + 3)^-1
= (x(4x - 3) + 4x2 + 7x + 24)((4x - 3) + 2x + 3)^-1 (from (i))
= (4x² - 3x + 4x² + 7x + 24)(6x)-1
= \(\frac{(8x^2 + 4x + 24)}{(6x)}\)
= \((\frac{8(4x-3)+4x + 24)}{(6x)})\) from (i)
= \(\frac{(32x - 24 + 4x + 24)}{(6x)}\)
= 6