First slide

Theory of expressions

Question

The roots $α, β$ of the equation $x^{2} - 5 x + a = 0$ are connected by the relation
$3 α + 2 β = 12.$ Then the value of $a$ is

Easy

A

$5$
B

$6$
C

$8$
D

$10$

Solution

The given equation is $x^{2} - 5 x + a = 0$
$α, β$ are the roots of given equation

Sum of the roots : $α + β = 5$ … ( 1 )

Product of the roots : $α β = a$ … ( 2 )

and $3 α + 2 β = 12$ … ( 3 )

Solving the first and third equations, we get

$α = 2 a n d β = 3$ and hence,

$α β = a \Rightarrow 2 (3) = a$

$∴ a = 6$

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