Question

If alpha and beta are the roots of the equation
x²- 5x + 6 = 0, then the value of alpha²- beta² is:
a. + -5
b.+ -13
c.+ -6
d. + -7​

Answer 1

Correct Question :-

If α and β are the roots of the equation x² + 5x + 6 = 0 ,find the value of α² + β² is :

a. ±5

b. ±13

c. ±6

d. ±7

Answer :-

b) ±13

Explanation :-

Given :-

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

So,

a = 1

b = -5

c = 6

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we know that :-

α+β = -b/a

αβ = c/a

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__________[Put values]

α+β = -(-5)/1 αβ = 6/1

α+β = 5 αβ = 6.......(ii)

α - β = -5......(i)

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A.T.Q

» α² + β²

[ by using identity (a-b)² = a² + b² -2ab]

» α² + β² = (α-β)² - 2αβ

» α² + β² = (-5)² - 2(6)

» α² + β² = ±(25 - 12)

» α² + β² = ±13

________________[Answer]