Question

If alpha and beta are the zeros of quadratic polynomial f(x) ax2+bx+c then evaluate alpha square and beta square

Answer 1

To FinD :

$\tt \dagger \: \: \: \: \: { \alpha }^{2} + { \beta }^{2}$

SolutioN :

We have, Quadratic polynomial.

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c.$

☛ We have,

☄ Sum of Zeros.

→ α + β = - b / a.

$\rule{90}2$

☄ Product Of Zeros.

→ α * β = c / a.

$\rule{90}2$

☯ Let's Find the value of,

$\tt : \implies { \alpha }^{2} + { \beta }^{2}$

☛ We have, Formula.

• a² + b² = ( a + b )² - 2ab.

$\tt : \implies {\bigg( \alpha + \beta \bigg)}^{2} - 2 \alpha \beta .$

$\tt : \implies {\bigg( \dfrac{ - b}{a} \bigg)}^{2} - 2 \bigg(\dfrac{c}{a} \bigg)$

$\tt : \implies \dfrac{{ b}^{2} }{{a }^{2} } - \dfrac{2c}{a}$

$\tt : \implies \dfrac{{b}^{2} - 2ac}{{a }^{2} }$

✡ Therefore, the value of required answer is b² - 2ac / a².

Answer 2

Step-by-step explanation:

QUESTION:-

If alpha and beta are the zeros of quadratic polynomial f(x) ax2+bx+c then evaluate alpha square and beta square

ANSWER:-

We have, Quadratic polynomial.

\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c.†ax 2 +bx+c.

☛ We have,

☄ Sum of Zeros.

→ α + β = - b / a.

☄ Product Of Zeros.

→ α * β = c / a.