JEE MAIN - Mathematics (2020 - 6th September Evening Slot - No. 16)
If $$\alpha $$ and $$\beta $$ are the roots of the equation
2x(2x + 1) = 1, then $$\beta $$ is equal to :
2x(2x + 1) = 1, then $$\beta $$ is equal to :
$$ - 2\alpha \left( {\alpha + 1} \right)$$
$$ 2\alpha \left( {\alpha + 1} \right)$$
$$2{\alpha ^2}$$
$$ 2\alpha \left( {\alpha - 1} \right)$$
Explanation
$$\alpha $$ and
$$\beta $$ are the roots of the equation
4x2 + 2x – 1 = 0.
$$ \therefore $$ $$\alpha $$ + $$\beta $$ = $$ - {1 \over 2}$$
$$ \Rightarrow $$ -1 = 2$$\alpha $$ + 2$$\beta $$
and 4$$\alpha $$2 + 2$$\alpha $$ - 1 = 0
$$ \Rightarrow $$ 4$$\alpha $$2 + 2$$\alpha $$ + 2$$\alpha $$ + 2$$\beta $$ = 0
$$ \Rightarrow $$ $$\beta $$ = $$ - 2\alpha \left( {\alpha + 1} \right)$$
4x2 + 2x – 1 = 0.
$$ \therefore $$ $$\alpha $$ + $$\beta $$ = $$ - {1 \over 2}$$
$$ \Rightarrow $$ -1 = 2$$\alpha $$ + 2$$\beta $$
and 4$$\alpha $$2 + 2$$\alpha $$ - 1 = 0
$$ \Rightarrow $$ 4$$\alpha $$2 + 2$$\alpha $$ + 2$$\alpha $$ + 2$$\beta $$ = 0
$$ \Rightarrow $$ $$\beta $$ = $$ - 2\alpha \left( {\alpha + 1} \right)$$
Comments (0)
