Question

If a and b are zeroes of polynomial 3x^2 + x + 2 then a^2 + b^2 =​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

GIVEN

a and b are zeroes of polynomial

$3 {x}^{2} + x + 2$

TO DETERMINE

${a}^{2} + {b}^{2}$

CALCULATION

Since a and b are zeroes of the given polynomial

So

$\displaystyle a+ b = - \frac{1}{3} \: \: and \: \: ab = \frac{2}{3}$

$\displaystyle {a}^{2} + {b}^{2}$

$= \displaystyle ( {a + b)}^{2} - 2ab$

$= \displaystyle {( \frac{ - 1}{ \: \: 3} )}^{2} - 2 \times \frac{2}{3}$

$= \displaystyle \frac{1}{9} - \frac{4}{3}$

$= \displaystyle - \frac{11}{9}$

Answer 2

Step-by-step explanation:

let a and b are the zeroes of the polynomials

3x²+x+2

a+b = -b/a

ab = c/a

a²+b² = (a+b)²-2ab

= (-b/a)² - 2×c/a

= ( -1/3)² - 2× 2/3

= 1/9 - 4/3

= 1-12/9 = -11/9