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The product of the roots of the equation : 1/2 x 2 - 5/4 x - 3=0

User Gatspy
by
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2 Answers

4 votes

Explanation:

(X-4)(2x+3)=0

X-4=0 2x+3=0

X=4 X=-3/2

User Vinu Prasad
by
8.3k points
2 votes

Answer:

Product of the roots of the equation
\bold{(1)/(2) x^(2)-(5)/(4) x-3=0} is -6

Solution:

If
\alpha and
\beta are the roots of any quadratic equation
x^(2)+b x+c=0 then,

Sum of roots
\alpha+\beta=-(b)/(a)

Product of roots
\alpha * \beta =
(c)/(a)

Given that


(1)/(2) x^(2)-(5)/(4) x-3=0

On simplifying the above equation,


(2 x^(2)-5 x-12)/(4)=0


2 x^(2)-5 x-12=0

Here a = 2, b = -5 and c = -12

So product of roots is
(c)/(a) that is
(-12)/(2) = -6

Hence product of the roots of the equation
(1)/(2) x^(2)-(5)/(4) x-3=0 is -6

User Walter Luszczyk
by
8.3k points

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