(D) Since the coefficients of the quadratic equation $x^2+ax+b=0$ are real,the complex roots must occur in conjugate pairs. Given that $1-i$ is a root

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(D) Since the coefficients of the quadratic equation $x^2+ax+b=0$ are real,the complex roots must occur in conjugate pairs. Given that $1-i$ is a root,its conjugate $1+i$ must also be a root of the equation. For a quadratic equation $x^2+ax+b=0$,the product of the roots is equal to the constant term $b$. Therefore,$b = (1-i)(1+i)$. Using the identity $(x-y)(x+y) = x^2-y^2$: $b = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2$. Thus,$b = 2$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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If $1-i$ is a root of the equation $x^2+ax+b=0$,then $b$ is equal to

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$1$
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$-1$
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$-2$
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$2$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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