If - and - are the zeroes of the polynomial - satisfying the relation- - - - then find the value of -

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Relations between Roots and Coefficients : Higher Order Equations

If 𝜶 and 𝜷 ...

Question

If 𝜶 and 𝜷 are the zeroes of the polynomial 𝒑(𝒙)= $2 x^{2} + 5 x + k$ , satisfying the relation, $α^{2} + β^{2} + α β$ = $\frac{21}{4}$ , then find the value of 𝒌.

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g (x) = x^{2} + 5 x + k

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The given pair of linear equations 𝟖𝒙 + 𝒒𝒚 = 𝟏𝟒 and 𝒑𝒙 + 𝟒𝟐𝒚 = 𝟒𝟗 has infinitely many solutions, find the value of 𝒌 if 𝒑 − 𝒒 = 𝒌.

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