Question

. If α and β are the zeroes of the polynomial 2

2− 13x + 6, then find α + β.​

Answer 1

Step-by-step explanation:

Answer:-

Given that:-

$2 {x}^{2} - 13x + 6$

We need to find the zeroes of the polynomial, and then sum it up. We will do it by Factorisation...

Why take so much hectic journey, when you have beautiful formulas for it?

And the magic formula is:-

$\alpha + \beta = \dfrac{ - b}{a}$

• Here, a is 2
• Here, b is -13
• Here, c is 6

$\alpha + \beta = \dfrac{ - ( - 13)}{2}$

$\alpha + \beta = \dfrac{13}{2}$

So, 13/2 is the required answer.

That's Not it!

What if we need to find the product of zeroes?

Simple, we do have a magic formula for this too. (This is not magic formula, we ought to apply it :D)

$\alpha \beta = \dfrac{c}{a}$

$\alpha \beta = \frac{6}{2}$

$\alpha \beta = 3$

So, for product of zeroes, 3 will be the answer.

Answer 2

Given:-

$\</u><u>b</u><u>i</u><u>g</u><u>star \: \text{2 - 13x + 6}$

To Prove:-

$</u>\bigstar\:<u> \alpha \: + \beta</u><u>\</u><u>:</u><u>=</u><u>\</u><u>:</u><u> </u><u>?</u><u>$

Solution:-

We Know that,

$\bigstar \text \: {\alpha \: + \beta \: = \frac{ - b}{a} \longrightarrow \: (1) } \\ \\ \bigstar \text \: a \: = 2 \\ \\ \bigstar\text \: b = - 13 \\ \\ \bigstar\text \: c \: = 6$

Substitute the value of b and a in equation (1)..

$\text \: \bigstar \:\alpha \: + \beta \: = \frac{ - ( - 13)}{2} \\ \\ \text \: \bigstar \: \alpha \: + \beta \: = \frac{13}{2}$

Hence Proved...