Question

if one root of the quadratic equation 3x2-px-2 = 0 is 2. then find p and another root.

Answer 1

3x∧2-px-2=0

1 root=2

3(2∧2)-2p-2=0
3*4-2=2p
2p=12-2
p=10/2
p=5
3x∧2-5x-2=0
3x∧2-6x+x-2=0
3x(x-2)+1(x-2)=0
(x-2)(3x+1)=0
x=-1/3(2nd root)

Answer 2

Given:

A quadratic equation,

$3x^{2} -px-2=0$

One root = 2

To Find:

The value of p and another root

Solution:

Putting x = 2 in the given quadratic equation

$3(2)^{2} -p(2)-2=0\\12-2p-2=0\\10=2p\\p=5$

To find another root, we put the value of p in the given quadratic equation

$3x^{2} -5x-2=0\\3x^{2} +x-6x-2=0\\x(3x+1)-2(3x+1)=0\\(x-2)(3x+1)=0\\x= -1/3$

Thus, x = -1/3 is the other root

Hence, p = 5 and x = -1/3 are the required answers.

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