Question

Q.14 If α and β are the zeroes of the polynomial 2x^2-4x+2, then the value of α+β is 2.

Answer 1

Answer:

Solution :-

Given Polynomial :-

2x² + 3x - 6

Roots = α and β

So as in a quadratic Polynomial :-

-b/a = Sum of roots = α + β

c/a = Product of roots = αβ

Now in our polynomial

a = 2

b = 3

c = -6

So

Sum of roots = -3/2

Product of roots = -6/2 = -3

Now we have to find out the value of

α² + β²

Now as we know

a² + b² = (a + b)² - 2ab

So

α² + β² = ( α + β)² - 2 (αβ)

= (-3/2)² - 2(-3)

= 9/4 + 6

= (9 + 24)/4

= 33/4

So α² + β²

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Step-by-step explanation: