Question

if alpha beta are the roots of x^2+3x-2=0 then a²+ß²​

Answer 1

EXPLANATION.

=> a, b are the roots of equation = x² + 3x - 2

To find the value of a² + b².

=> sum of roots of equation

=> a + b = -b / a = -3/1

=> a + b = -3 .......(1)

=> products of roots of equation

=> ab = c/a = -2

=> ab = -2 .......(2)

Formula of a² + b².

=> ( a² + b² ) = ( a + b)² - 2ab

=> ( -3)² - 2 ( -2)

=> 9 + 4 = 13

Therefore,

=> a² + b² = 13.

Answer 2

Answer:

➡️ Solution ⬅️

x²+3x-2 = 0

where, a = 1, b = 3, c = -2

☯️ Sum of the roots = a+ß = - $\dfrac{b}{a}$

=> - $\dfrac{3}{1}$ = -3

☯️ Product of the roots = aß = $\dfrac{c}{a}$

=> $\dfrac{-2}{1}$ = -2

◀️ According to the question,

Formula used:-

⭐ (a²+b²) = (a+b)² - 2ab ⭐

=> (-3)² -2 (-2)

=> 9+4 = 13

✔️ Hence, the value of a²+ß² = 13

Step-by-step explanation:

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