Question

if alpha and beta are the zeros of quadratic polynomial f x is equals to ax square + bx + c then evaluate Alpha square+ beta square​

Answer 1

Answer:

Now solving the quadratic equation for sum of roots and product of roots we get

$\alpha + \beta = - b \div a \\ \alpha \beta = c \div a \\ \\ \\ ( \alpha + \beta ) {}^{2} - 2 \alpha \beta = \alpha {}^{2} + \beta {}^{2} \\ \\ ( - b \div a) {}^{2} - 2c \div a = \alpha {}^{2} + \beta {}^{2} \\ \\ \alpha {}^{2} + \beta {}^{2} =( b {}^{2} - 2ac) \div a {}^{2}$

Step-by-step explanation:

As sum of roots is - b/a

And product of roots is c/a

And (a+b) ^2-2ab=a^2+b^2

Answer 2

Given:-

f(x) = ax²+bx+c = 0

To find:-

α² + ß²

α+β = $\sf\dfrac{-b}{a}$

αß = $\sf\dfrac{c}{a}$

Identity:-

$\underline{\boxed{\sf α²+ß² = (α+ß)²-2αß}}$

Solution:-

$\implies$ (α+ß)²-2αß

$\implies$ ${\bigg(\sf\dfrac{-b}{a}\bigg)}^{2}$ - $2 \times \bigg(\sf\dfrac{c}{a}\bigg)$

$\implies$ $\sf\dfrac{b²}{a²}$ - $\sf\dfrac{2c}{a}$

$\implies$ $\sf\dfrac{b²-2ac}{a²}$