Solve the equation
Given that roots are a+1,a-1,b+1,b-1
Answers
Answer:
x
4
+10x
3
+35x
2
+50x+24.
Step-by-step explanation:
x
4
+10x
3
+35x
2
+50x+24=x
4
+(x
3
+9x
3
)+(9x
2
+26x
2
)+(26x+24x)+24
=(x
4
+x
3
)+(9x
3
+9x
2
)+(26x
2
+26x)+(24x+24)
=x
3
(x+1)+9x
2
(x+1)+26x(x+1)+24(x+1)
=(x+1)(x
3
+9x
2
+26x+24)
=(x+1)(x
3
+(2x
2
+7x
2
)+(14x+12x)+24)
=(x+1)((x
3
+2x
2
)+(7x
2
+14x)+(12x+24))
=(x+1)(x
2
(x+2)+7x(x+2)+12(x+2))
=(x+1)(x+2)(x
2
+7x+12)
=(x+1)(x+2)(x
2
+3x+4x+12)
=(x+1)(x+2)(x(x+3)+4(x+3))
=(x+1)(x+2)(x+3)(x+4)
Answer:
x^4 – 10x^3 + 35x^2– 50x + 24 = 0
Factor:
(x - 1) (x^3 - 9x^2 +26x - 24)
(x - 1) (x - 2) (x^2 - 7x + 12)
(x - 1) (x - 2) (x - 3 )(x - 4)
Answer is x = 1, 2, 3, or 4