Question

if alpha and beta are the zeros of quadratic equation x² -2x +3 then alpha ²+ beta ² is​

Answer 1

Step-by-step explanation:

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

$\alpha \times \beta = \frac{c}{a} = 3$

${ \alpha }^{2} + { \beta }^{2} = ( \alpha + \beta )^{2} - 2 \alpha \beta$

${2}^{2} - 2 \times 3$

$4 - 6 = - 2$

Answer 2

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Given,

Equation p(x) = x² - 2x + 3

We have to find :

α² + β²

Solution :

α² + β² = (α + β)² - 2αβ

We know that,

For a quadratic polynomial,

α + β = -b/a

= -(-2)/1

= 2

αβ = c/a

= 3/1

= 3

α² + β² = (α + β)² - 2αβ

= (2)² - 2(3)

= 4 - 6

= -2

Therefore, α² + β² = -2