Question

If one root of quadratic equation 2x^2– px + q = 0 is 2 + under root3 (p,q  rational numbers), then p/q equals to-
(1) 2
(2) 3
(3) 4
(4) 8

Answer 1

hello frd......
may be (3)is the correct ans hope it's help u ..

Answer 2

Answer:  The answer is (3) 4.

Step-by-step explanation: Given that one root of the quadratic equation $2x^2-px+q=0$ is (2 + √3).

We are given to find the value of "p divided by q."

We know that the irrational roots occur in pairs, so the other root of the equation will be (2 - √3).

Now, the sum of the roots is given by

$-(-\dfrac{p}{2}})=(2+\sqrt 3)+(2-\sqrt 3)\\\\\Rightarrow \dfrac{p}{2}=4\\\\\Rightarrow p=8,$

and the product of the roots is given by

$\dfrac{q}{2}=(2+\sqrt3)(2-\sqrt3)\\\\\Rightarrow \dfrac{q}{2}=4-3\\\\\Rightarrow \dfrac{q}{2}=1\\\\\Rightarrow q=2.$

Therefore,

$\dfrac{p}{q}=\dfrac{8}{2}=4.$

Thus, (3) is the correct option.