Question

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

Answer 1

Step-by-step explanation:

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

X-4=0 2x+3=0

X=4 X=-3/2

Answer 2

Answer:

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

Solution:

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

Sum of roots $\alpha+\beta=-\frac{b}{a}$

Product of roots $\alpha \times \beta$ = $\frac{c}{a}$

Given that

$\frac{1}{2} x^{2}-\frac{5}{4} x-3=0$

On simplifying the above equation,

$\frac{2 x^{2}-5 x-12}{4}=0$

$2 x^{2}-5 x-12=0$

Here a = 2, b = -5  and  c = -12

So product of roots is  $\frac{c}{a}$ that is $\frac{-12}{2} = -6$

Hence product of the roots of the equation $\frac{1}{2} x^{2}-\frac{5}{4} x-3=0$ is -6