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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If fx = x2 - ...

Question

If f(x) = x $^{2}$ - 2x + 1 and g(x) = x $^{3}$ - 2x $^{2}$ + 1, find f(x) + g(x).

^{3}

- 2x

^{2}

- 2x + 2

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^{3}

- x

^{2}

- 2x + 2

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^{2}

- 2x + 2

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^{3}

- x

^{2}

- 5x

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Solution

The correct option is B x $^{3}$ - x $^{2}$ - 2x + 2
Given: f(x) = x $^{2}$ - 2x + 1 and g(x) = x $^{3}$ - 2x $^{2}$ + 1

f(x) + g(x) = (x $^{2}$ - 2x + 1) + (x $^{3}$ - 2x $^{2}$ + 1)
f(x) + g(x) = x $^{3}$ + (x $^{2}$ - 2x $^{2}$ ) - 2x + 2
f(x) + g(x) = x $^{3}$ - x $^{2}$ - 2x + 2

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If f(x) = x2 - 2x + 1 and g(x) = x3 - 2x2 + 1, find f(x) + g(x).

The correct option is B x3 - x2 - 2x + 2Given: f(x) = x2 - 2x + 1 and g(x) = x3 - 2x2 + 1 f(x) + g(x) = (x2 - 2x + 1) + (x3 - 2x2 + 1) f(x) + g(x) = x3 + (x2 - 2x2) - 2x + 2 f(x) + g(x) = x3 - x2 - 2x + 2

If f(x) = x $^{2}$ - 2x + 1 and g(x) = x $^{3}$ - 2x $^{2}$ + 1, find f(x) + g(x).

The correct option is B x $^{3}$ - x $^{2}$ - 2x + 2
Given: f(x) = x $^{2}$ - 2x + 1 and g(x) = x $^{3}$ - 2x $^{2}$ + 1

f(x) + g(x) = (x $^{2}$ - 2x + 1) + (x $^{3}$ - 2x $^{2}$ + 1)
f(x) + g(x) = x $^{3}$ + (x $^{2}$ - 2x $^{2}$ ) - 2x + 2
f(x) + g(x) = x $^{3}$ - x $^{2}$ - 2x + 2