Question

for what value of a and b the equation x^2-(2a-3)x=3b+4 should have both the roots zero​

Answer 1

Answer:  The required values of a and b are

$a=\dfrac{3}{2},~~b=-\dfrac{4}{3}.$

Step-by-step explanation:  We are given to find the values of a and b for which the following quadratic equation will have both the roots equal to 0 :

$x^2-(2a-3)x=3b+4~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

in a quadratic equation, both the roots are equal to zero if the coefficient of x term and the constant term both are zero.

So, for equation (i) to have both the roots zero, we must have

$-(2a-3)=0\\\\\Rightarrow 2a-3=0\\\\\Rightarrow 2a=3\\\\\Rightarrow a=\dfrac{3}{2}$

and

$3b+4=0\\\\\Rightarrow 3b=-4\\\\\Rightarrow b=-\dfrac{4}{3}.$

Thus, the required values of a and b are

$a=\dfrac{3}{2},~~b=-\dfrac{4}{3}.$

Answer 2

Step-by-step explanation:

For the roots to be equal to zero, the coefficient of x and constant must be zero.