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Formation of a Quadratic Equation From It's Roots

If α and β ar...

Question

If α and β are the zeros of the quadratic polynomial f(x) = x² − 5x + 4, find the value of $\frac{1}{α} + \frac{1}{β} - 2 αβ$ .

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Solution

Sinceand are the zeros of the quadratic polynomial

Therefore

=

= 5

We have,

By substituting and we get ,

Taking least common factor we get ,

Hence, the value of is.

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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