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Grade 11Algebra

In the equation a4x^4 + a3x^3 + a2x^2 + a1x + a0 =0 roots of equation are ai ,i =1,2,3,4. Now x is replaced by x – 1 ,now roots of new equation are

muktesh singh

11 Years agoGrade 11

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student
Please find the answer to your question below,
$a_{4}x^{4} + a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0} = 0$
a₁, a₂, a₃& a₄are the root of this equation.
$a_{4}(a_{i})^{4} + a_{3}(a_{i})^{3}+a_{2}(a_{i})^{2}+a_{1}(a_{i})+a_{0} = 0$
Now for the equation,
$a_{4}(x-1)^{4} + a_{3}(x-1)^{3}+a_{2}(x-1)^{2}+a_{1}(x-1)+a_{0} = 0$
Put
$x = a_{i} + 1$
$a_{4}(a_{i}+1-1)^{4} + a_{3}(a_{i}+1-1)^{3}+a_{2}(a_{i}+1-1)^{2}+a_{1}(a_{i}+1-1)+a_{0} = 0$ $a_{4}(a_{i})^{4} + a_{3}(a_{i})^{3}+a_{2}(a_{i})^{2}+a_{1}(a_{i})+a_{0} = 0$
So the roots of new equaion are
a₁+1, a₂+1,a₃+1, a₄+1

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