Grade 11Algebra

Solve the following equations :

x^4 – 2x^3 + 4x^2 + 6x – 21=0

x^4 – 2x^2 + 8x – 3=0

muktesh singh

12 Years agoGrade 11

1 Answer

SHAIK AASIF AHAMED

11 Years ago

Hello student,
Please find the answer to your question below
1.x⁴-2x³+4x²+6x-21=0
x⁴-2x³=-4x²+6x-21
Adding x²on both sides we get
(x²-x)²=-3x²-6x-21
(x²-x+y)²=x²(-3+2y)+x(-2y-6)+y²+21
by putting y=2 we get perfect square on RHS
so (x²-x+2)²=(x-5)²
it is in the form of a²-b²=0
Hence we get a+b=0;a-b=0
so x²-3=0 and x²-2x+7=0
we get x= $\pm \sqrt{3}$ ,1 $\pm \sqrt{6}i$
(2) let x⁴-2x²+8x-3=(x²+ax+b)(x²+cx+d)
we get on solving a=-2,b=3,c=2,d=-1
So x⁴-2x²+8x-3=(x²-2x+3)(x²+2x-1)
on solving above 2 quadratic equations we get x= $\sqrt{2}-1$ , $-\sqrt{2}-1$ , $1-\sqrt{2}i$ , $1+\sqrt{2}i$