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If α and β are the zeroes of a Quadratic polynomial x2 + 3x + 6. What is the value of α2 + β2

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a

2

b

-

2

c

3

d

-

3

answer is D.

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Detailed Solution

Now the given equation is x2 + 3x + 6
Now we know if α and β are the roots of the equation ax2 + bx + c = 0 then the sum of roots α + β is given by −

\frac{b}{a}

and the product of the roots is given by

\frac{c}{a}

Hence comparing it with the equation x2 + 3x + 6 we get
α + β = −

\frac{3}{1}

= −3.............(1)
αβ =

\frac{6}{1}

= 6.....................(2)
Let us find, α2 + β2
We know that a2 + b2 + 2ab = (a+b)2
This means α2 + β2 + 2αβ = (α+β)2
Hence α2 + β2 = (α+β)2 − 2αβ
Now substituting the values from equation (1) and equation (2) we get.
α2 + β2 = (−3)2 − 2(6)
α2 + β2 = 9 – 12
α2 + β2 = −3
Hence, option (4) is the correct option.

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If α and β are the zeroes of a Quadratic polynomial x2 + 3x + 6. What is the value of α2 + β2