Question

if alpha and beta are zeros of quadratic 3 x square - 5 x + 1 then form quadratic polynomial whose zeros are Alpha square plus beta square

Answer 1

Hey!!

Let alpha and beta be the zeroes of given quadratic polynomial.


Given quadratic polynomial

$3x {}^{2} - 5x + 1 = 0$

On comparing with ax^2 + bx + c = 0 we get

a = 3

b = - 5

c = 1

Sum of zeroes = - b / a

$= > \alpha + \beta = \frac{ - ( - 5)}{3} \\ \\ = > \alpha + \beta = \frac{5}{3}$

Product of zeroes = c / a

$= > \alpha \times \beta = \frac{1}{3}$

$\alpha {}^{2} + \beta {}^{2}$

Using identify ( a + b ) ^2 = a^2 + b^2 + 2ab


$= > ( \alpha + \beta ) {}^{2} + 2 \alpha \beta \\ \\ = > ( \frac{5}{3} ) {}^{2} + 2 \times \frac{1}{3} \\ \\ = > \frac{25}{3} + \frac{2}{3} \\ \\ = > \frac{25 + 2}{3} \\ \\ = > \frac{27}{3} \\ \\ = > 9.$

Hope it helps!