Question

If α, β are the roots of the equation x² + α x + β = 0, then
the values of α and β are
(a) a = 1, B = -1 (b) a = 1, B = -2
(c) a = 2, B = 1 (d) a = 2, B = -2

Answer 1

Question:

If @ and ß are the roots of the equation

x² + @x + ß = 0 , then the values of @ and ß are :

a) @ = 1 , ß = -1

b) @ = 1 , ß = -2

c) @ = 2 , ß = 1

d) @ = 2 , ß = -2

Answer:

b). @ = 1 , ß = -2

Note:

• The general form of a quadratic equation is ;

ax² + bx + c = 0.

• If A and B are the roots of the given quadratic equation ax² + bx + c = 0 , then ;

Sum of roots , (A+B) = -b/a

Product of roots , (A•B) = c/a

• If A and B are the roots of a quadratic equation then the equation is given as :

x² - (A+B)x + A•B = 0.

Solution:

Here,

The given quadratic equation is :

x² + @x + ß = 0

Clearly,

Here we have ;

a = 1

b = @

c = ß

Also,

It is given that , @ and ß are the roots of the given quadratic equation , thus ;

Sum of roots = -b/a

=> @ + ß = -@/1

=> @ + ß = -@

=> ß = - @ - @

=> ß = -2@ ------(1)

Also,

Product of roots = c/a

=> @•ß = ß/1

=> @ = ß/ß

=> @ = 1

Now,

Putting @ = 1 in eq-(1) , we have ;

=> ß = -2@

=> ß = -2•1

=> ß = -2

Hence,

@ = 1 and ß = -2

Answer 2

Answer:

$\large\boxed{\sf{(B)\;\alpha=1,\;\beta=-2}}$

Step-by-step explanation:

It's being gven that,

α, β are the roots of the equation x² + α x + β = 0.

To find the value of α and β.

We know that , general formual of a quadratic equation is given by,

• ax² + b x + c = 0

Now, comparing the given equation with general equation, we get,

• a = 1
• b = α
• c = β

Now, we know that,

Sum of roots = -b/a

=> α + β = -α/1

=> α + β = - α

=> 2α = - β .........(1)

And, also, we know that,

Product of roots = c/a

=>α β = β/1

=> α β = β

=> α = 1

Substituting this value in eqn (1), we get,

=> β = - 2 × 1

=> β = -2

Hence, the correct option is (B) α = 1, β = -2