Question

If 2x^2-7x+3=0 and 4x^2+ax-3=0 have a common root then find the values of a?
find this and earn 20 points but not blam nonsense answer​

Answer 1

Answer:

The values of a are 4 and -11

Step-by-step explanation:

First we find the roots of $2x^2-7x+3=0$

$2x^2-7x+3=0$

$2x^2-6x-x+3=0$

$2x(x-3)-1(x-3)=0$

$(2x-1)(x-3)=0$

$x=\frac{1}{2},3$

case(i): 3 is a common root

Then,

$4(3)^2+a(3)-3=0$

$36+3a-3=0$

$33+3a=0$

$3a=-33$

$\implies\:a=-11$

case(ii): $\frac{1}{2}$ is a common root

$4(\frac{1}{2})^2+a(\frac{1}{2})-3=0$

$4(\frac{1}{4})+\frac{a}{2}-3=0$

$1+\frac{a}{2}-3=0$

$\frac{a}{2}-2=0$

$\frac{a}{2}=2$

$\implies\:a=4$