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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 p(x) = 4x² − 5x − 1, find the value of α²β + αβ².

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Solution

Since and are the zeros of the quadratic polynomials

Sum of the zeros =

Product of zeros =

We have,

By substituting and in, we get

Hence, the value of is.

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Q. The zeros of

P (x) = 3 x^{2} - x - 4

α

β

.Then find the value of

α^{2} β + α β^{2}

α

β

are the zeros of the polynomial

p (x) = x^{2} - 5 x + k

α - β = 1

k

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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