Question

If alpha and bita are the zeroes of the polynomial 2x²+7x+5,write the value of
$\alpha + \beta + \alpha \beta$
​

Answer 1

AnsWer :

- 1.

Correct QuestioN :

If α and β are the zeroes of the polynomial 2x² + 7x + 5, write the value of α + β + α * β.

SolutioN :

We have, Polynomial.

→ 2x² + 7x + 5.

☛ Compare With General Expression.

→ ax² + bx + c.

Where as,

• a = 2.
• b = 7.
• c = 5.

✎ Sum of Zero.

→ α + β = - b / a.

$\rule{90}2$

✎ Product Of Zero.

→ α * β = c / a.

$\rule{90}2$

So,

$\tt \longmapsto\alpha + \beta + \alpha \beta = ?$

$\tt \longmapsto\dfrac{-b}{a}+ \dfrac{c}{a}$

$\tt \longmapsto\dfrac{-7}{2}+ \dfrac{5}{2}$

$\tt \longmapsto \dfrac{-7+5}{2}$

$\tt \longmapsto \dfrac{-2}{2}$

$\tt \longmapsto- 1.$

✡ Therefore, the value of α + β + α β = - 1.

Answer 2

$\bf\large{\underline{Question:-}}$

If alpha and bita are the zeroes of the polynomial 2x²+7x+5,write the value of

$\alpha + \beta + \alpha \beta$

$\bf\large{\underline{Given:-}}$

• 2x²+7x+5

$\bf\large{\underline{To\:find :-}}$

• $\alpha + \beta + \alpha \beta$

$\bf\large{\underline{Solution:-}}$

we know ,

A general quadratic equation is

$\tt→ax^2+bx+c$

Where are a,b and c are numeric values.

Now,

From the given equation.

$\tt→ 2x^2+7x+5\\\tt→ a=2\\\tt→b=7\\\tt→ c=5\\\tt→ Sum\:of\:zeroes = \alpha+\beta\\\tt→ \alpha+\beta=\frac{-b}{a}\\\tt→ \frac{-b}{a}=\frac{-7}{2}\\\tt→ product\:of\:zeroes =\alpha\beta\\\tt→ \alpha\beta=\frac{-c}{a}\\\tt→ \frac{c}{a}=\frac{5}{2}$

So,

$\tt→\alpha+\beta+\alpha\beta=?\\\tt→ \frac{-7}{2}+\frac{5}{2}\\\tt→ \frac{-7+5}{2}\\\tt→ \frac{-2}{2}\\\tt→ \alpha+\beta+\alpha\beta=-1$

Hence,

$\large\tt→{\underline{\fbox{\red{\alpha+\beta+\alpha\beta=-1}}}}$