Question

if alpha and beta are the zeros of the quadratic polynomial 2x^2-5x+7,then find the value of alpha+beta-3alpha beta

Answer 1

Given polynomial :-

$2x {}^{2} - 5x + 7$

Sum of zeroes

$\alpha + \beta = \frac{ - b}{a}$

$= > \alpha + \beta = \frac{ - ( - 5)}{2} \\ \\ = > \alpha + \beta = \frac{5}{2}$

Product of zeroes

$= > \alpha \beta = \frac{c}{a} \\ \\ = > \alpha \beta = \frac{7}{2}$

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$\alpha + \beta - 3 \alpha \beta \\ \\ = > \frac{5}{2} - 3( \frac{7}{2} ) \\ \\ = > \frac{5}{2} - \frac{21}{2} \\ \\ = > \frac{5 - 21}{2} \\ \\ = > \frac{ - 16}{2} \\ \\ = > - 8.$

$\textbf{Hope it helps!}$