Question

alpha and beta are the zeros of the polynomial 2 x square - 4 x + 5 find the value of Alpha square + bita square

Answer 1

Hey mate..
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Given,

α and β are the zeroes of the polynomial $2x {}^{2} - 4x + 5$

We know,

$\alpha + \beta = \frac{ - b}{a} \\ \\ = \frac{ - ( - 4)}{2} \\ \\ = \frac{4}{2} \\ \\ = 2$

Also,

$\alpha \beta = \frac{c}{a} \\ \\ = \frac{5}{2}$

Now,

$\alpha {}^{2} + \beta {}^{2} \\ \\ = ( \alpha + \beta ) {}^{2} - 2 \alpha \beta \\ \\ = (2) {}^{2} - 2 \times \frac{5}{2 } \\ \\ = 4 - 5 \\ \\ = - 1$

Hope it helps !