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The polynomial `f(x)=x^4+a x^3+b x^3+c x+d`has real coefficients and `f(2i)=f(2+i)=0.`Find the value of `(a+b+c+d)dot`A. 1B. 4C. 9D. 10 |
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Answer» Correct Answer - 3 If a polynomial has real coefficients then roots occur in complex conjugate and roots are 2i -2i, 2 + I,2-I Hence ,f(x)=(x+2i)(x-2e)(x-2-i)(x-2+I)` `f(1)=(1+xi)(1-2i)(1-2-i)(1-2+i)` `f(1)=5xx2=10` Also, f(1)= 1+a+b+c+d` `therefore 1+a+b+c+d=10` `rArr a+b+c+d=9` |
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