Question

find a so that the sum and product of the roots of equation 2x^2+(a-3)+3a-5=0 are equal​

Answer 1

SOLUTION :-

TO DETERMINE :-

The value of a so that the sum and product of the roots of the below equation are equal

$\sf{2 {x}^{2} + (a - 3)x + (3a - 5) = 0}$

EVALUATION

Here the given equation is

$\sf{2 {x}^{2} + (a - 3)x + (3a - 5) = 0}$

Now

The sum of the roots of the equation

$\displaystyle \sf{ = - \frac{(a - 3)}{2} }$

The products of the roots of the equation

$\displaystyle \sf{ = \frac{(3a - 5)}{2} }$

Now it is given that, the sum and product of the roots of the equation are equal

$\therefore \: \: \: \displaystyle \sf{ - \frac{(a - 3)}{2} = \frac{(3a - 5)}{2} }$

$\implies \sf{ - (a - 3) = (3a - 5)}$

$\implies \sf{ - a + 3 = 3a - 5}$

$\implies \sf{ - 4a = - 8}$

$\implies \sf{a = 2}$

FINAL ANSWER

Hence the required value of a is 2

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Additional Information

A general equation of quadratic equation is

$a {x}^{2} + bx + c = 0$

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

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