Question

2.
9
Alpha and Beta are the zeroes of the polynomial x²+6x +
5 then a² + B² + 2a B =​

Answer 1

Answer

The value of α² + β² + 2αβ is 36

$\bf\large\underline{Given}$

The quadratic polynomial is :

• x² + 6x + 5
• α and β are the zeroes of the polynomial

$\bf\large\underline{To \: Find}$

• The value of α² + β² + 2αβ

$\bf\large\underline{Solution}$

Given,

The zeroes of the polynomial x² + 6x + 5 are α and β

We know that ,

$\sf sum \ of \ the \ zeroes = -\dfrac{coefficient \ of \ x}{coefficient \ of \ x^{2} }$

$\sf\implies \alpha + \beta =-\dfrac{6}{1} \\\\ \sf\implies \alpha + \beta = -6 \\\\ \sf\implies (\alpha + \beta)^{2} = (-6)^{2} \\\\ \sf\implies \alpha^{2} + \beta^{2} + 2\alpha\beta= 36$

Hence , required value is 36