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Write a polynomial function in factored form with double roots at -2 and 5 and the constant term of the polynomial in standard form is -40.

User Ossek
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1 Answer

4 votes

Answer:


f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40

Explanation:

If -2 and 5 are double roots of the polynomial function, then the function expression is


f(x)=a(x-(-2))^2(x-5)^2\\ \\f(x)=a(x+2)^2(x-5)^2

Rewrite this function in standard form:


f(x)=a(x^2+4x+4)(x^2-10x+25)\\ \\f(x)=a(x^4-10x^3+15x^2+4x^3-40x^2+100x+4x^2-40x+100)\\ \\f(x)=a(x^4-6x^3-21x^2+60x+100)\\ \\f(x)=ax^4-6ax^3-21ax^2+60ax+100a

The constant term of the polynomial in standard form is -40, so


100a=-40\\ \\a=-(40)/(100)=-0.4

Therefore, the function expression is


f(x)=-0.4x^4-6\cdot (-0.4)x^3-21\cdot (-0.4)x^2+60\cdot (-0.4)x+100\cdot (-0.4)\\ \\f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40

User Sumbul
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